Bus routes and guided busways will have been gradually converted into tram systems following the widespread success of examples such as Croydon Tramlink. Even Edinburgh.
might have a working system. This may lead to considerations for extra heavy rail lines within cities being dropped.
A railway line linking mainland Europe and Ireland via the west coast of England or Wales may have been built, leading to high-speed stations en-route. Perhaps a new line will have been built as a branch off HS2 (which, by the way, will involve fewer reversals after better designs for stations have been drawn up).
More and more services outside London and big cities will operate on a turn-up-and-go frequency due to population increases causing demand; hopefully more reliable signalling and better braking/acceleration will help.
There will probably be a number of lines that have finally been built connecting up nearby branches and termini.
You will find a "further out" version of the London Overground, with new lines going east-west south of the Croydon area, for example, and perhaps a parallel of the Varsity Line closer to London.
London will be a mass of incredibly complex railway systems. Londoners will barely remember which layer is actually the "ground" because the whole city - buildings, transport etc. - are stacked on top of each other even more than ever. The "Underground" is a quaint and old-fashioned term.
Someone will have increased the North Downs Line, Redhill to Tonbridge, Southeastern Mainline gauges and ensured electrification throughout. Cross-country services will use the line between the southeast and the west side of the UK.
Ticketing will be simpler and pay-by-mile at the same rate throughout the country. Peak restrictions probably won't exist but there may well still be First Class - possibly even a Business Class option, too.
More services will have small shop/buffet counters.
You'll find the odd Turbostar and Turbo Express on heritage railways as these have recently been scrapped...
The last Pacer has disintegrated into a pile of dust.