It is certainly possible if you are a bit flexible in locations. I personally would limit it to either Ireland, or England, Scotland and Wales, just to avoid the flight or ferry involved in traveling between the islands. But that just my personal bias.
Let’s say you choose England/Scotland——these are places we (my husband and I ) like a lot, and I would be comfortable traveling solo here. The Scots in particular are just about the friendliest people I have met in my travels. It is pretty easy to travel around both countries by train, although there have been some strikes that can interfere with your plans (that is where the need for flexibility comes in). I am confident that people here can help you build an itinerary that minimizes big cities and maximizes smaller towns and villages, and countryside with scenery and sacred sites.
I will start by suggesting a resource that we use, a sort of tour company but actually it is a member-owned cooperative that offers walking and special interest holidays at their country houses all over the UK. Non-members are welcome to join their holidays. Their main focus is guided walking, but they also offer sightseeing holidays, and special interest ones focused on yoga and wellness, choral singing, bridge, writers’ workshops, photography, birding. . . You name it.
You could book one (or two) of these short holidays in places that interest you, and then combine those with independent travel to other places of interest.
Here is an example, a 3-night “Discovery” holiday in the Scottish Highlands that has availability in June:
https://www.hfholidays.co.uk/holidays-and-tours/3-night-scottish-highlands-discovery-tour?format=pdf&vid=459
Here is a list of “island hopping” sightseeing tours in Scotland, the Channel Island, and England (Isle of Scilly):
https://www.hfholidays.co.uk/holidays-and-tours#/holidays?FC.Holiday%20Types=Island%20hopping&sort=ordering%7CASC&page=1
(I did not vet those for availability in June). They also offer week-long “discovery” tours in areas such as Cornwall, the Lake District, Northumberland, and more, and of course their regular “guided walking” holidays at their own locations around the UK (but you did not mention walking/hiking among your interests so I did not suggest any of these, but there are lots of options with availability if you are interested).
A basic itinerary for the UK would be to fly into London, then loop up to Scotland via York and surrounding areas, spend a week or so there, then return to London via the Lake District, Cotswolds, Cornwall, and more, perhaps spending your last night before flying out in Windsor, close to Heathrow.
