That just won't work, people simply won't wear it, especially if there's leisure use taking place. What happens if a train is cancelled or taken out of service for whatever reason?
I can really see trains being a problem. This week I've been working at a slightly different time to normal, which combined with some early-morning engineering work on my route means I've been going in on a train which I wouldn't normally use (which in fact wouldn't exist in the normal timetable, although a similar service would). The normal timetable service I speak of would I believe be a 12-car class 700, GTR in their infinite wisdom are currently running an 8-car 2x387. To be fair this is adequate, but there isn't much scope for it to be much busier than it is now (I'd say about 10 people per carriage by the last stop before London) before distancing will break down.
Furthermore, there's people doing unhelpful things like sticking themselves in an aisle seat right in the middle thus taking up more "distancing space" than they need to, or sitting opposite someone else so they can use a plug socket, plus the usual few who just have to walk to the front before arrival at the terminus and then crowd around the front doorways. It would only take one infected person to cough a few times and it's easy to see how a whole batch of people are liable to become infected. On that score I suspect use of masks may have to be made compulsory just to give some extra protection, as I don't think distancing alone is going to prove workable.
As regards booking, how are you going to physically prevent people boarding a service they're not booked on?