Hi Weaver, welcome to the forum.
Do a search on this - there was great discussion a while ago about a similar event across the Irish Sea.
The possibly bigger issue you may have in the channel might be likened to a sponsored chicken crossing the road - where the Irish sea is an empty A- road in the highlands and the channel is like crossing the M25...... (I refer of course to the passing traffic - not the distance paddled!)
I believe Dover - Calais might be the shortest crossig - 22 nautical miles (approx) so a rib with reasonable fuel capacity could motor itself back. in an hour or so (weather permitting!) I guess you would need something with a cabin / 1st aid etc 'coz you can bet your house if something goes the way of the pear, it will happen mid channel......