I work on the two out of three plan for long water crossings:
1. lifejacket
2. immersion suit
3. raft
Unless crossing the N.Atlantic when it's all three.
For the channel, a lifejacket (worn!) is fine.
It is exceptionally unlikely that you'll end up in the water during the few minutes the crossing takes, and even if this does happen you'll almost certainly be able to ditch near a small boat/yacht who can come and pick you up.
Be realistic about the odds of disaster.
Don't worry about it, go!
Fly (safe!), Sam.