In 1940, the British had no adequate, organised air-sea rescue plan. The RAF relied on the hope that a passing trawler or Naval vessel would pick up any downed pilots. A fair number were picked up by the RNLI ( Royal National Lifeboat Institution ) who played an unsung role in the Battle.
A conference in 1939 had placed the responsibility for organising air-sea rescue under Coastal Command ; some launches had been ordered but were not ready in time for the Summer of 1940.
The RAF fighter pilots had no dinghies or fluorescent dye markers ; all they had was the 'Mae West' lifejacket. The temperature of the Channel in Summer reaches about 14 degrees C at best giving a downed pilot about 4 hours before death from hypothermia ( this of course varied depending on the individual, there are instances of pilots surviving 12 hours or so ).
A further horror was the standard issue Van Heusen shirt ; the collar shrank in contact with salt water and could choke the unfortunate wearer. This is the main reason for RAF pilot's unofficial adoption of the white silk scarf ; it wasn't just because they looked
ASR definitely 'caught the British out' during the BofB ; on 22 August 1940 Fighter Command got 12 Lysanders to help with sea searches, but many pilots drowned within sight of the shore. Possibly the worst place to be shot down was the Thames estuary; the swift currents made survival virtually impossible.
The proper, RAF Air-Sea Rescue organization was formed in 1941.
( The above details come from various sources, including Bungay, The Most Dangerous Enemy , Price, The Hardest Day, and Mason, Battle Over Britain ).
( PS : TA, the North Sea is definitely more inhospitable than the Channel. The Channel does at least benefit from the very tail-end of the current from the Gulf of Mexico : even so I wouldn't like to be adrift in either place...
As for the RNLI it saved some 6 500 people during the war years but I haven't found any stats on RAF pilots. Another interesting thread