We did many trips to the UK before we moved here, always renting a cottage and doing walks from there. It is my favorite way of walking because you can take a day off when you need it, you can make your own coffee every morning and I can cook our dinners. I can see the appeal of Inn to Inn walking, but it isn't for us.
The warmest part of the UK is London and the southeast (Kent, Sussex, Hampshire). The next warmest is the southwest (Dorset where we live, Devon and Cornwall). Devon can get a lot of rain in the winter - more than Cornwall I think. Dorset is dryer than Devon and Cornwall. Our neighbor has a palm tree.
There is a lot of walking in our area and the local buses are good. You could be based near Bridport and walk the coast path from Exmouth to Poole using your car and buses or taxis to return to it. We did this on the Cotswold Way and we have done this for parts of the South Coast Path here. Plus there are many circular hikes off the Coast Path, or inland.
I would love to see you both again and we could do some of the walks together.
Here is a cottage that we rented and liked:
Sweetbriar Cottage from Dream Cottages.
Here is my list of agencies for Dorset.
If you decide to come here, I can do some searching and checkout cottages. I think there are some in our village (Bothenhampton). From here you can walk into Bridport (30 mins) or to West Bay on the sea (30 mins).
I post photos nearly every day on
Instagram and they share with my
Slow Europe page on Facebook. You could have a look back to last October to see what the weather was like.