I live in Leicester, so I have the same problems with getting to the coast. I haven't really been out locally and just do as Fenlander has suggested and go on holiday somewhere good (Cornwall and the south west has a lot of estuaries, which often have good boat ramps and facilities).
I have also looked at Blakeney / Morston etc and have been put off by the mud. You are either going for a very short trip (maybe 1hr either side of high water) or a full 10-12hr trip, else risk having to drag the boat back through some mud. Of course until you actually do it, you don't know how much window you have. I might be being pessimistic with my 1hr either side of HW assessment. Maybe there is 2-3hrs each side of HW before the slipway turns to mud. Someone needs to be a good egg and take one for the team and report back
The one favorable thing about the east coast, is that it is generally in the lee of the prevailing wind. So more often than not the sea will be fairly flat. Whereas in the south west, I would say that more often than not the sea is not flat! For these reasons I would like to find a decent launch site on that side of the country.
While searching for options, you can also look on
Boatlaunch
Good luck.