There is very little true competition on UK railways. Most services are run on Government-granted franchises which give a monopoly or at best a duopoly on specific routes.
There are a handful of open-access train operators who operate outside the franchises, but they can't just decide to compete on a route if that route is already covered by a franchise.
To create true competition, the infrastructure and stations would need to be taken into public ownership and the train operators would run whatever services they see fit.
> To create true competition, the infrastructure and stations would need to be taken into public ownership and the train operators would run whatever services they see fit.
The problem with that is that on a mixed-traffic railway it's very easy to run out of capacity once you have a mixture of trains with differing stopping patterns (and perhaps some freight on top) running along the same line. Once you reach that point, competition stops being directly about passengers and starts being about train paths, which can have rather annoying side effects for passengers.
Plus connections don't really work well with competition, either, because a) that'd require coordination between possibly differing operators, which is anathema to unfettered competition, and b) where a regional feeder route might only run hourly or half-hourly, it's impossible to have good connections with more than one or at most two sets of connecting trains anyway.
(Also c) through-ticketing with sufficient passenger rights in case you miss a connection enroute – at least the UK kept a national ticketing system even throughout privatisation and including all open-access operators, whereas in Germany it's an incompatible free-for-all, despite a legal obligation for railway companies to ostensibly offer through-tickets.)
There are a handful of open-access train operators who operate outside the franchises, but they can't just decide to compete on a route if that route is already covered by a franchise.
To create true competition, the infrastructure and stations would need to be taken into public ownership and the train operators would run whatever services they see fit.