I love Bath and have spent up to 5 nights at a time there, but in my opinion it is not quiet. It's certainly smaller than London but it is busy. If you choose Bath I would make sure not to visit on a weekend. Quiet places there- Prior Park but it's an uphill walk to the entrance and then you are mostly downhill once you're inside. There is a really neat Palladian Bridge in the garden which is what I went specifically to see. Parade Gardens which are right in the center of Bath along he river but you pay a nominal entry fee and it's surprisingly quiet in there.
Do you have a Jane Austen interest? One year I timed my visit for the first weekend of the JA Festival in Sept which was such fun! I love that time period and got a huge laugh out of seeing all the participants dressed in costume. I did do some of the associated activities with the Festival.
Bath is easy by train from London and there is a National Express bus to Heathrow.
Have you considered Salisbury? I find it quieter than Bath. I love the Cathedral there ( has one of the Magna Cartas) as well as the Cathedral Close. The Wessex Museum on the Close is small but very interesting and has many Stonehenge artifacts. There is a public bus route from the City Center to Stonehenge and Old Sarum if that's of interest. You can also walk thru the water meadows where Constable did a number of his paintings. The B&B I stay in there is inexpensive and excellent. The last time the owner marked out a walking route for me thru the meadows. I really enjoy Evensong at the Salisbury Cathedral. It's very intimate and feels like a worship service (which of course it is) more than a tourist attraction which is the feeling I get at Westminster Abbey. I've sat and read at benches in the meadows. Not sure about bookshops.
I've taken the train from London to Salisbury. Not sure about transport to one of the airports but as I was walking around I did see a National Express coach stop.
I've been to the Lake District on a Rick Steves tour. I enjoyed Keswick but I felt it was very outdoors oriented. I did walk from the City Centre out to Castlerigg Stone circle (path no longer there that I walked on as part was destroyed by flood) and it was a pretty tedious uphill walk - similar to Prior Park in Bath. There was a nice path around Derwentwater but it was pouring rain. We also did a boat ride but again, pouring rain so did not get off at any of the optional stops.
I'll have to check out that blog as I'm not familiar with it so thanks for the tip.
There was a thread on Trip Advisor's London forum recently asking about quiet spots. One of the suggestions is The Wetlands Centre which I am going to try and work in next visit. I'll go for the birding!