Here are two sites I often use close to where I live in South Devon. Both are free to use by the public.
The first is at Teignmouth, close to the docks at the sand quay, is handy being near a car park, and good for all states of the tide. It's a hard sand and gravel beach, not too steep for my Volvo tow car. The Teign is a lovely sheltered estuary opening onto a spectacular coastline of red sandstone cliff and numerous beaches. Several of the beaches are only accessible by boat. The railway follows along the shoreline here, between Dawlish Warren and Teignmouth.
Another favourite slip is at the Steamer Quay, Totnes, Devon, and again it is usable at any state of the tide. The car park adjacent can fill by 10am at weekends, so plan to get in early if you can. There is also a caravan club site within ½ mile. This is at the head of the River Dart Estuary and the run to Dartmouth takes about two hours each way (6 knots max). The wildlife and scenery is really beautiful all the way.

If I can offer any further guidance to any club member who wishes to explore the area do feel free to email me at - tappergraham@gmail.com

I have stumbled upon this web site that lists boat launch locations throughout the UK. I cannot not vouch for its accuracy so please use it with caution. However, it is clearly a useful starting point when investigating where may be possible to access waterways and you can then dig deeper for current local conditions/byelaws/safety issues etc before committing to a trip or any risks.

https://www.boatlaunch.co.uk/

It would be interesting if Graham could locate his suggested locations on this web site to see if it gives good information?