English Countryside Getaway near London - No Car

Richmond and Richmond Park or Chiswick and walk along the Thames River path. Or train to Whitsable or Rye.

Try the Chilterns which are accessible by public transport from London

https://www.chilternsaonb.org/visit-chilterns/market-towns/

You could take the coach (bus) from Heathrow to Oxford. Oxford is a city, but not a very large one. There will be hotels, inns, and Airbnbs there, some on the outskirts of Oxford. You could take walks through the countryside or walk along the river through beautiful natural scenery to a pub for lunch or dinner.

Or....you could take the bus to Oxford from Heathrow, then immediately do a short train ride to Moreton-In-Marsh, a small village in the Cotswolds. Lots of countryside there. Moreton will have hotels and some Airbnbs. Moreton is one of the pick up points for a day tour of the Cotswold villages. We used Go Cotswolds for a one day tour and were very pleased with the experience.
https://www.gocotswolds.co.uk/product/cotswolds-in-a-day/

You wrote:
"I've come across plenty of Airbnbs that seem lovely, but am not confident on where would be the best location to fit our needs."

Could you share some of these with us and perhaps we can give our opinions on them.

There is Sevenoaks, with Knole House on its doorstep. The house is open and is well worth visiting. It is surrounded by a large deer park which is open dawn to dusk . It's onlyt a short train journey from London

The English countryside in November can be wet and miserable - it’s dark by 4pm. If you want cafes, pubs and supermarkets with access to public transport, you need a small town, not a village. Many village pubs and shops have closed.

My suggestions would be quaint Stamford in Lincolnshire where Middlemarch was filmed; Tring in Hertfordshire with access to the Chiltern hills; Sevenoaks in Kent with a day trip to nearby Canterbury; Lewes in Sussex with its castle and access to Brighton and the coast; and Petworth in Sussex with its antique shops and Petworth House.

In addition to Airbnb, you could try a couple of other reliable sites: Vrbo and Cottages.com. I have used both and had no problems. Look for accommodation with a good heat source. It will be chilly and damp that time of year and dark early. Your question makes me think of the cottage in the Movie The Holiday! (if you haven't seen it then it is a good Christmas movie).

I like Rebecca’s suggestion of Moreton-in-Marsh, it’s wonderful, has everything you asked for, and is in the charming Cotswolds with lots of lovely walking opportunities.

I was just in Rye and Petworth, they were just ok imo.

November isn’t a great time to visit the Cotswolds - no colour in the gardens and some places will be closed for the winter. Public transport isn’t great either - an area best seen with a car.

I don’t use Airbnb these days as their charges are high. Booking.com, Trip Advisor rentals and VRBO are better options.

Petworth is one of the most desirable (and expensive) places to live in England! Each to their own - I think the Cotswolds are over rated by members of this forum.

The Cotswolds villages are charming and lovely all year round, there’s no equivalent here in the US which makes them special for most of us.

The village of Lacock is quaint and close to Georgian city of Bath and not long on train to London!

I’d recommend Bruton in Somerset. It’s a 2hr direct train journey from London and is a small, charming town with more than enough pubs and restaurants to keep you nicely entertained for a week. Lovely countryside walks around.