One thing the Government could do fairly easily is to remove the vast majority of competition law as applied to public transport services. What's "anticompetitive" in say supermarkets is very often to the passenger's benefit in public transport operation - given how little on-road/on-track competition there is, far more people would benefit from "collusion" of transport operators than would lose by fares going up a bit as two operators agreed their level and interavailability.
It also extends to timetables, the journey I made today is a good example, at the moment the 'timetable planets' are in alignment:
Walk 7 mins
Train 25 mins Change, wait 5 mins Train (different TOC) 17mins
Wait 7 mins, short (5min) bus ride to save 25min walk
The reverse journey is similar
When the timetables work out journey door to door takes about 1h 20m which is competitive with driving, which will take a good hour, as roads are busy single carriageways with a lot of 30/40mph speed limits (also quite a tedious drive, and plenty of opportunity for further hold ups particularly in Summer), but when timetables change some of the waits increase to 50mins, and then driving becomes the better option. Problem is you have 2 different TOC and a bus company involved.
Ticket wise 2 separate rail tickets are required, for an £11 return fare (Off peak return end to end is £18) and a £1.70 bus fare.
Ideally GBR should try and align timetables to maintain connections, and bus companies should align their services with the rail ones. Its not just about competition, to me until public transport is properly integrated it will always be patchy and will not acheive its full potential even at current levels of service (and therefore is not delivering best value for money in terms of subsidy). This probably means some level of 'nationalisation', and as for the fares system, well I think everyone agrees its broken, it has certainly cropped up in this thread a number of times.