Country walking tours in England?

There are several Walking or Hiking Tours in the Cotswolds online. This area has "the" quaint villages, scenery etc. Some friends of mine did one that made lodging arrangements ahead of them and ferried their luggage. I'm sure that you will get some recommendations to follow.

Are you planning on just walking for the day?
If you are looking for 3 or 4 or 5 day trip,
I would recommend HF Holidays. The company offers dozens of tours all over UK.
I loved my tour of the Cotswolds - stayed in Burton on the Water and we were in Harrington House.
You can pick guided or self-guided walks .
The guided are led by The Ramblers and that was my choice.

HF Holidays Site

We used Contours Walking Holidays for our self-guided walks. Contours took care of the overnight B&B bookings, arranged luggage transfers and provided maps, guidebooks and walking instructions/advice. England is big into walking and there are many other reputable walking companies that other walkers seemed to be happy with. A number of the UK walkers did it (bookings) all on their own.

I've heard good things about HF Holidays from UK walkers. HF Holidays offer guided walks and tend to base camp (sleep in the same bed for several nights) at one of their holiday lodges. Just need to keep up with the UK walkers.

60s is still young for walkers. We encountered a group of women on our Coast to Coast that we referred to as the Aussie Grannys. The group of six grandmother like women were doing the Coast to Coast walk with their husbands driving and transferring the luggage. The walked the same distances that we walked pacing us for a week or so, but had an extra layover day.

Booking companies have suggest itineraries ranging from long mileage days to shorter distance walking days and will custom schedule layover days. Some will also have bail out options of riding with the luggage if someone needs the day off or doesn't want to brave a heavy rain day.

Check out the various walking holiday companies such as Contours for suggested walking itineraries. They offer walks from epic multiple week walks to short 2 day holidays. For example:
https://www.contours.co.uk/walking-holidays/circular-walks-cotswold.php#COTSB
https://www.contours.co.uk/walking-holidays/south-west.php

When my husband and I were 60, we did a 4-day self-guided walk to/from Bath which was organized by Cotswold Walks (http://www.cotswoldwalks.com). They offer many different routes for different distances and days. I found them very easy to work with and would go again. The walking along the right of way, using the directions provided, was a highlight of our trip; it was a truly unique experience walking right through the middle of cultivated fields on the small path that is part of the Right of Way. Each day offered amazing scenery, quaint villages, and a challenge -- it was like a treasure hunt! We got off track a time or two but figured it out and got back on the right path without much problem. Check them out!

This one might be a little arduous for you. Friends of ours in their late 60s took it last spring and loved it, but found it pretty strenuous, and they're serious walkers. I understand there are more and less challenging options for most days, i.e. you can do the whole walk or ride partway.

Another possibility might be along Hadrian's Wall, which you could customize to your time and capacity.

We used Andrew Guppy, Cotswold Walks, last August. We spent 8 nights in the Cotswolds.

Thank you all for your advice. We're looking forward to our adventure. - Alan