I travelled from Lincoln to Richmond, Surrey and back a couple of weeks ago and it was one of the nicest trips I've ever taken. Allocated seating, at least 2m apart, on the train to Kings Cross and very few people travelling so it was blissfully peaceful and I didn't see anyone without a mask/covering.
The suburban train to Richmond was also quiet and around 95% of those I saw had their faces covered. The return trip was much the same.
I have to qualify this by saying that I don't have the sort of health conditions which might add to concerns and I have been somewhat dismissive throughout of the panic and alarm about public transport which has been engendered in so many people.
However, I have never seen the trains so clean as they are at present; station staff are politely reminding people to stay apart. My feeling is that if the OP follows the rules, avoids the rush hour, carries and uses hand cleanser, then there's no reason not to take a train journey.