Cotswolds

Moreton-on-Marsh is accessible. the problem comes when you try to get by public transportation to the other towns which is the real draw of the Cotswolds.

If you don't want to drive then you might consider staying in bath and doing a day tour from there to the Cotswolds. there are a few companies that do this. Mad Max and City of Bath Guides are two that I know of.

I would think again and go back to your first idea of Bath. The Cotswolds is a large area of mainly small villages and a couple of places that might just about qualify as towns (Stow on the Wold for example). However, it is not at all easy to explore on public transport. You could get to Moreton on the Marsh by train, but I'd struggle to find much to do there for more than about an hour. I used to live on the edge of the Cotswolds in Worcestershire and while there are some lovely spots and great walks, and also some nice stately homes to visit, it's really not at all public transport friendly. Bath on the other hand is easily reached by train from London and has lots to keep you entertaining for a day or so.

Morten in Marsh in the Cotswolds. 2hours by train. Or Oxford. Oxford is about an hour and a half from Paddington.

Have you thought of heading to a seaside spot?

Whitsable? Margate? Eastbourne? Brighton?

Lastly, a pleasant London neighborhood is Highgate which you could explore the Highgate Wood. There’s also the Highgate cemetary where Karl Marx is buried. I believe you now need to book a tour in order to meander in cemetary but I could be wrong.
Highgate is pleasant neighborhood that good majority of tourists are unaware of. If you like seeing venerable pubs, the Winchester is a short stroll from the Highgate station.

We took the train from London Paddington to Moreton-on-Marsh then the bus to Stow-on-the-Wold to use as a home base. It was very easy. We then spent the next 4 days walking or using the bus to visit different villages before returning to London. The local TI was great with maps and suggested routes.

For a short trip Moreton is just fine. There is fairly decent bus service to some of the main villages - Broadway and Chipping Campden one way (Stagecoach buses), Stow and Bourton the other way (Pulham buses).

Short train ride to Oxford. A stop or two before Oxford is Hanborough station; from here a walk or short bus ride to Blenheim Palace and the village of Woodstock, both worth a visit.

A few things to do in and around Moreton itself. If you are up for a fairly easy hike, Batsford Arboretum, Bourton House and Sezincote can all be reached on foot.

Regarding the buses, anyone who hasn't used Pulhams this year, since Easter, has out of date information. Since they were taken over by the Oxford Bus Company service frequencies have been very significantly enhanced and there is now integrated ticketing with Oxford Bus Company services. Timings at Moreton in Marsh have also now been matched with train times.

It is also never mentioned on here that it is entirely possible, on Stagecoach, to do a day trip to Stratford on Avon from Moreton, also that it is possible to reach Chipping Norton (and thus other Cotswolds destinations) by bus from Oxford.

While train from Oxford to Moreton in Marsh is faster and more frequent there is that other route, especially if there is a problem with the trains.