Jonny
Another suggestion that is not quite what you outlined as you requirement.
You state that your boat cannot stay at the River Axe.
So a first part of your requirement might be somewhere to move the boat to at least initially possibly not too far from the Axe. And you state that you want a marina, not say just a mooring.
You might look at Dolphin Boatyard at the head of Galpmton Creek off the River Dart. It is say three coastal day sails from the Axe.
What was Dolphin boatyard on the South of the creek has recently bought what was Dartside Quay on the North of the creek and it is now one business administered from Dartside Quay. They have added a number of new pontoon berths in the middle of the creek. The new pontoons are all walk ashore and have water and electricity on the pontoons. They all dry out but are accessible for a few hours either side of high water.
The annual charge for a 27 foot boat is £2,952 inclusive of Value Added Tax. (£8 per day.) That is not cheap , but it is cheaper than any other marina on the Dart. I didn't enquire about shorter stays.
Jeff Middleton a JRA member who lives in the North of England, had booked his boat into Dolphin last year in order to cruise the South coast for at least a season. Unfortunately he lost his boat en-route .... (That children is another story!)
An advantage of Dolphin would be that you can move your boat onto the drying out pad on the quay wall of the old boatyard to dry out for underwater work. I have done that with Lexia for a number of years now. Cheap compared with the cost of a lift out and lift in. Water and electricity available on the quay for pressure washing.
The River Dart is one of the most beautiful rivers imaginable. Galmpton Creek is quiet and sheltered. It would be very suitable for staying on the pontoon over winter. Dolphin has all the facilities that you might require and lots of trades available for support if required. Galpmton village has a good community owned shop and a good pub.
This is not an upmarket MDL marina , and all the better for that. (However, if you want that plus a town then look at Brixham or Torquay.)
However, Paignton, the nearest station takes from 3 to 3 1/2 hours from London. Then a bus and a walk to the boatyard, or a taxi.
Cruising the South West peninsular from the Dart is wonderful. And the Channel Islands are approximately 70 miles away (a dawn to dusk day sail in summer) and Roscoff in Britanny is 100 miles away (a 20 hour overnight sail) both achievable solo if need be. And if you are intending to head for Southern Europe, Dartmouth is a good departure , or day sail to Falmouth for an departure into the Western Approaches.
Just a thought ......
Jonathan