Sgt C.Haig of No 604 Squadron was on night patrol on the 25th of August 1940 and crashed in a Blenheim I (L6782) near Exeter. His pilot (J.G.B.Fletcher) and the other crew member (A.L.Austin) were killed.
On the afternoon of 10 May 1940 P/O Richard Haine flew one of the six Blenheim's of No 600 Squadron which attacked Waalhaven aerodrome, Rotterdam, in daylight. Only one Blenheim returned from the mission. Haine claimed a Bf 109 destroyed and two Ju52's damaged before he was shot down and made a force-landing in Holland. He and his gunner, P/O M.Kramer, and the CO's navigator, Sgt Davis, evaded capture and made it back to England.  For this action Haine received the D.F.C. on the 9th of July 1940.
Sergeant J.K.Haire of No 145 Squadron on the 27th of October 1940  in his Hurricane I (V6888) ditched on the sands of Bembridge and escaped injury after a dogfight with a Bf 109 at 17:15hrs. J.K.Haire was promoted to Pilot Officer. He was K.I.A. on the afternoon of the 6th of November he baled out of his Hurricane I (V6627) too low after combat over the Isle of Wight.
F/Lt N.M.Hall of No 257 Squadron was shot down in his Hurricane I (P2981) and killed over the Channel by a Bf 109 of JG 27 on the 8th of August 1940 at 12:00hrs.
P/O R.M.D.Hall  volunteered for Fighter Command after Army training in a tank Regiment.He flew some 40 sorties in Spitfire's with No 152 Squadron.
P/O Herbert James Lamprier Hallowes joined the R.A.F. as an apprentice. He qualified for his wings and joined No 43 Squadron in early 1940. He shared a He111 on the 3rd of February 1940, and on the 4th  of April 1940 damaged another. He added to his score on the 1st of June when he shot down three fighters. On the 7th of June he was about to bale out of his burning Hurricane (N2585) when a Bf 109 overtook him. He sat back in his cockpit, and shot the Bf 109 down, then baled out, dislocating his ankle on landing. On the 8th of August, Hallowes shot down two Bf 109's. On the 13th he shot down three bombers. He scored another 8 kills before the end of the month. His total score was 17 confirmed an 2 shared. He went on to command No 222 Squadron, No 165 Squadron and No 154 Squadron. Hallowes was awarded the D.F.M. and Bar on the 6th of September 1940.
Sgt D.W.Halton from No 615 Squadron was shot down and killed in his Hurricane I (P2801) by a Bf 109 on the 15th of August 1940 at 12:05hrs.
Sgt. P.Roger E. de Cannart d'Hamale was the first Belgian to pilot to reach British soil. He arrived on the 20th of June 1940. He was posted to No 46 Squadron flying Hurricane's. He baled out of his Hurricane I (VB6549) unhurt on the 11th of September 1940 at15:30hrs. He had been in combat over Bodiam. Kent.
P/O A.C.Hamilton of No 141 Squadron was the gunner in a Defiant (L7009) flown by Flt/Lt I.D.G.Donald.Their aircraft was shot down by a Bf 109 of JG 51 near Dover on the 19th of  July 1940 at 12:45 hrs. They both perished.
F/Lt Harry Raymond Hamilton a Canadian of No 85 Squadron was shot down and killed on the 29th of August 1940 at 18:15hrs. His Hurricane I (V6623) shot down by a Bf 109 near Rye.
Sgt Ronnie F.Hamlyn joined No 610 Squadron on the 6th of June 1940 he was 23 years old. Hamlyn destroyed two enemy aircraft before the 24th of August. On the 24th of August he destroyed a Ju 88 and four Bf 109's.
Hamlyn then destroyed Bf 109's on the 26th, 27th, 28th and the 30th of August. Hamlyn was awarded the D.F.M. on the 13th of September 1940 and the A.F.C. on the 1st of January 1943.He rose to the rank of Wing Commander.
Pilot Officer Osgood "Pedro" Hanbury flew with No 602 Squadron during the Battle of Britain in a Spitfire (X4882).
P/O Norman Patrick Watkins 'Pat' Hancock was born on the 4th of August 1919, Pat Hancock joined the RAF on a short service commission on the 6th of February 1939. He joined No 266 Squadron at Sutton Bridge on the 7th of November 1939. He was sent to Berry-au-Bac in France where he joined No 1 Squadron. On August the 16th 1940, flying from Northolt, he was in combat with an Me 110 over the South Downs. His Hurricane was damaged but he returned to his base. On the 30th of August his Squadron was scrambled to intercept a raid over Essex at about 16:30hrs. He claimed a probable He 111.
Sgt. Bruce Hancock (742644) was a trainee bomber pilot in a Avro Anson and he saw a Heinkel bomber attacking a small airfield in Gloucester (Windrush) on the 18th of August 1940.  The Heinkel then turned towards the Anson  (N9164) attacking it. Hancock turned off his landing lights an when the bomber closed to about 150yds Hancock banked violently to port and flew into the the path of the Heinkel. Hancock died in the impact as did the crew of the Heinkel. 
Eye witnesses on the ground said that Hancock deliberately rammed the Heinkel.

I have included him because i think he was a very brave pilot and  deserves some recognition for his selfless act.
F/O D.H.W.Hanson of No 17 Squadron was killed on the 3rd of September 1940 at 10:55hrs. He baled out of his Hurricane I (P3673) after shooting down a Do 17. He struggled to get out of his Hurricane  and when he did, he was too low and his parachute failed to deploy. He hit the ground from around a hundred feet on Foulness Island.
Sgt O.Hanzlicek a Czech of No 312 (Czech) Squadron was killed on the 10th of October 1940. His Hurricane I (L1547) caught fire in the air and he baled out but died. His Hurricane I crashed into the River Mersey off Ellsmere Port.
F/O John R.Hardacre of No 504 Squadron was killed on the 30th of September 1940. His Hurricane I (P3414) was shot down in combat off Weymouth, Dorset at 17:00hrs.
P/O R.Hardy from No 234 Squadron was in combat with a Bf 109 on the 15th of August 1940 at 18:30hrs. He force landed his Spitfire I (N3277) at Cherbourg and was made a P.O.W.  His aircraft was captured intact by the Germans.
P/O F.N.Hargreaves of No 92 Squadron was killed on the 11th of September 1940 at 16:15hrs. His Spitfire I (PK9793) was shot down off Dungeness.
P/O C.S.Harrisonof No 238 Squadron was killed on the 28th of September 1940 at14:50hrs. His Hurricane I (V6778) was shot down by a Bf 109 over the Solent.
P/O J.H.Harrison joined No 145 Squadron in early August. Following a combat on the 12th of August 1940 at 12:30hrs with Bf 110's and Ju 88's South of the Isle of Wight was shot down in his Hurricane I (R4180) . Harrison was reported M.I.A. aged 22.
P/O F.C.Harrold of No 501 Squadron was killed on the 28th of September 1940 at 10:10hrs. His Hurricane I (P3417) was shot down by a Bf 109 near Deal in Kent.
P/O K.G.Hart of No 65 Squadron was attacked by a Bf 109 on theon the 20th of August 1940 over the Thames Estuary at 15:30hrs. His Spitfire I (R6818) was badly damaged and written off but he escaped injury.
P/O D.Hastings flew with No 74 Squadron in Spitfire's during the Battle of Britain. He was killed in a mid air collision with P/O Buckland. 
Sgt. Ralph (Titch) Havercroft flew Spitfire I (N3249) with No 92 Squadron during the Battle of Britain. His score was 3 destroyed 1 shared and 2 unconfirmed. 
P/O John Kenneth Haviland an American was born on the 19th of January 1921 in Mount Kisco, New York. He spent most of his early life in England, starting school there at the age of five. John went to Nottingham University at 17. He obtained his 'A' Licence and joined the R.A.F.V.R. He was called up at the outbreak of war and was posted to I.T.W. at Pembroke College, Cambridge in November 1939. After completing his flying training he went to the No 1 School of Army Co-operation, Old Sarum. He volunteered for Fighter Command, was posted to No 6 - O.T.U. Sutton Bridge in August 1940 and after converting to Hurricanes joined No 151 Squadron at Digby on the 23rd of September 1940. The following day, the 24th of September he collided with another Hurricane during formation practice and made a forced-landing in a paddock at Waddington. He was awarded the D.F.C. on the 16th of February 1945, as a Flight Lieutenant with No 141 Squadron.
Sgt R.P.Hawkings joined No 601 Squadron in June 1940. He scored 1 kill on the 17th of July 1940. Sgt RP Hawkings was K.I.A. on patrol over Sussex on the 18th of August 1940 at 14:50hrs in a Hurricane I (L1990) and was shot down by a Bf 109 from JG 27, he was aged 22.
Sgt F.B.Hawley joined No 266 Squadron in early July 1940. Following the destruction of a Heinkel He115 floatplane on the 15th of August off Dunkirk he is believed to have crashed his Spitfire(N3189)  into the sea off Deal, Kent at 17:15hrs and was reported M.I.A., aged 23.
F/O J.F.J.Haworth from No 43 Squadron flying a Hurricane I (P3964) was killed  baling out at 18,000ft after combat on the 20th of July 1940 at 18:00hrs.
On the 10th of May F/L T.Norman Hayes and his gunner (G.H.Holmes) flew one of six Blenheim's from No 600 Squadron which attacked Rotterdam airfield in daylight on the 10th of May 1940. His aircraft was the only one of the six to return to base and he was awarded the D.F.C. on the 24th of May 1940. Holmes was also later awarded the D.F.M.
F/O  James C.F.Hayter was born in Timaru, New Zealand on the 18th of October 1917. He attended Nelson College from 1928 to 1934. Working on farms and sheep stations, he took flying lessons with the Marlborough Aero Club as money and time allowed. In 1938 he joined the R.N.Z.A.F. and began his flying training at Wigram. Hayter sailed for the U/K in July to join No 98 Squadron, a light bomber unit equipped with Fairey Battles. In the November of 1939 Hayter was posted to No 103 Squadron in France, initially flying Battles on reconnaissance. On the 12th of May 1940, Hayter found himself piloting one of three Battles sent to attack river bridges and roads near Sedan. After shaking off some attacking Bf 110's, the three aircraft flew along the River Meuse in line astern to attack a German pontoon bridge with their gunners firing at enemy troops along the banks. The successful bombing of the bridge held up the advance of German tanks for some hours. He was shot down on the 16th of June 1940 by a Bf 109 as he was about to land and later on the same day the unit was withdrawn to England. In early September Hayter volunteered for Fighter Command and joined No 615 Squadron, moving two weeks later to No 605 Squadron. During October 1940 he damaged a Ju 88 and two Bf 109's. On the 26th of October 1940 he was attacked at 25000 feet and his Hurricane I set on fire. Slightly wounded, Hayter baled out of his Hurricane I (P2916)  after combat with a Bf 109 at 15:45hrs. He landed in the grounds of a house where a cocktail party was taking place. He was invited to join it and was later picked up by his fiancée, who lived not far away. He was awarded the D.F.C. in October 1941 and was awarded a Bar to the D.F.C. in January 1945. He ended the war with nine victories, returning to New Zealand in September 1945 to resume farming.