On a Le Touquet trip last week I did a 'practice lost procedure' with my student off the dover coast, I then asked 121.5 how long it would take to get a helicopter to us mid channel?
Answer: Search and Rescue Heli would be crambled from Lee on Solent, taking up tp 15 mins, plus transit time.
I would say Lee On Solent to Dover area could take at least 25 mins by Heli, so you could be swimming for 40 mins. In the winter the chances are you would be dead from exposure without an imersion suit or getting into a raft.
(I suspect the French have SAR in Calias possibly quicker to mid channel?).