Trains or car.

Yes, you can do this without a car. We have made several trips around England, Scotland, and Wales using the trains and a bus or taxi or two, and have found it fun and enjoyable. And you definitely do not want a car I n London anyway.

The train does not go to Fowey, but you can go as far as Bodmin Parkway, and take a bus or taxi from there. We did that a few years ago to reach Port Isaac, which is the same distance from Bodmin Parkway, and it was easy. Or perhaps your travel companion’s family will have other suggestions (like meeting you at the train and driving you to Fowey).

We did four weeks in southern Wales and England in October 2017 with a rental car. We didn't visit London or a major city, except Cardiff and York.

The British countryside is amazing. While you can do it by train, I think that you would miss quite a lot by using that method of transport.

We have driven in the UK twice with a rental car and managed well driving on the left. The key is to don't be in a hurry, stick to the speed limits and pay attention where you are going, especially when turning at intersections. British drivers are largely polite and follow the rules.

We visited Bath, the Cotswolds (you really need a car for that) at Chipping Camden (used it as a base to visit Oxford, Blenheim Palace and Stratford Upon Avon) as well as Winchester, Warwick Castle, York, the Yorkshire Moors, Whitby, Durham, Hadrian's Wall and the Lake District. In Wales, we visited Tintern Abbey, other castles, Cardiff, the Museum of Welsh Life, Tenby, St. David's and the village in SW Wales where my paternal ancestors came from.

Here is my detailed review of our trip with places, places we lodged and dine, etc. It may be helpful to you.
https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=599139

Most of it would be doable by train. You might look for a Cotswolds tour from Bath -- not as satisfying as driving yourself, but much easier. In Wales, places like Cardiff and Swansea would be easy but rural areas more difficult. For Cornwall, best to put yourselves in the hands (and car) of your companion/s relatives.

I like driving and do a lot of road trips, but left-side driving has been more of a challenge for me than I'd expected. I understand your reluctance to try it. But maybe you could try a rental from Bath to see the Cotswolds over a couple of days. It might not be as uncomfortable as you expect. An automatic shift will cost more but give you one less "different thing" to think about.

A personal preference question. We get a rental car because we tend to stop at small places between places that would be hard to get to via public transportation, or, would take a lot of time to get to because of the public transportation schedules. To me, the Cotswolds, Cornwall, and possibly southern Wales depending on where you intend to go, are best seen with a rental car. As already mentioned, you don’t need a car in London

Thank you all for your thoughtful responses, and, in particular, geovagriffith for including your itinerary!
Your responses confirmed my suspicions that we should consider renting a car for at least part of the trip. I’ll give it some careful thought as I would be the driver - my sister-in-law will not want to drive at all.

You can do almost all of that by train - which would be my personal preference. Especially these days, with petrol edging ever closer to 2 GBP/litre. As the others have said, the most difficult part would be the Cotswolds, but that is easily addressed by either a tour from Bath, or perhaps a 2-3 day car hire from Bath. I'd much rather have someone else do the driving while I watch the scenery go by, have a beverage, stretch my legs. If you do end up driving, please know that in London a car is an expensive proposition aside from just being a general pain.