Slow travel in England, but where??

For one of the places, I would choose somewhere near Carlisle, or also along the Hadrian's Wall route. I really enjoyed the area, and enjoyed all of the walks that I took.

For another week I would likely choose Wales instead of England, staying somewhere like Bangor with great transit connections, and visit more castles, explore, and walk.

I'd go with Wales and Scotland! The Snowdonia area of Wales is lovely and peaceful. We loved Betws-y-Coed. Aviemore, Scotland is also lovely and has great things to do.

We just returned from Cornwall and it was so beautiful.
We did have a car so I don't really know about public
transportation. Very relaxing

I would spend a week in the Cotswalds and the other week in Cornwall.

I would suggest one week in Cornwall. Choose the location carefully if you want to do lots of day trips. Somewhere closer to the Devon border than to Penzance would give you a lot more options. For the second week, go to Yorkshire. Besides the Dales, you can visit York, many monasteries and castles, and beautiful coastline around Whitby. I think you will be very inconvenienced in the countryside without a car. Relying on public transportation will waste a lot of your precious vacation time.

How about Dorset? Lots of lovely old villages, (although you'd have to check on what the public transport is like) and the coast is a beautiful area to walk. Maybe use Dorchester or Weymouth as a centre.

Alternatively, Devon and Cornwall, both really pretty counties (very popular in the summer).

Both areas are accessible by train or bus from London.

Northern Wales is absolutely glorious. Castles, hills, lakes, small villages, a chance to hear Welsh Gaelic, and delightful people. "Betsy-Coed" (never did get the spelling or pronunciation) is, as has been said truly beautiful. And we're going to be in Scotland a second time in May. The western islands (e.g., Arran, Skye, Islay) are truly places to unwind, walk, slow down, and enjoy. Then again, a couple of years ago, when we were driving (in pouring rain) on a one-lane road on the northern end of Skye, not having seen a human being or a house in a long time, we met a FedEx truck coming towards us.

I would echo the recommendations for the Cotswolds - you can easily walk from one village to another in some areas. Rick Steve's says you can even get a taxi back, but we haven't tried that. There is minimal, but some bus service.