They should create a Crossrail/Tube-type of network in the big cities, and then link them up to a high speed service. Having just got back from a trip to the East of France, I had forgotten how pleasant trains could be (I used to use them all the time in Europe) with a decent infrastructure.
The TGV was hitting speeds of 322 Km/h and was so smooth you forgot you were on a train. The seats were comfortable, the cabins spacious, we had wifi, and charging points. Heck even the "slow" double decker trains were pootling at over 160km/h with complete comfort.
Fast inter-city connections are excellent in Europe and are beneficial, and what's crazy is that the time it took us to get from London to almost the German border took as much time as it would have to have taken the train from London to Edinburgh.
Europe has got it right - the UK are trying to catch up. Perhaps they're not going about it the right way, but the UK desperately needs better infrastructure, and the problem is all the lines they currently have is poor and not up to spec. Rather than doing patch-work improvements, it's better to either rip it all out and start again, or just build a new network which is better using innovative technologies. Transport, and rail and construction industries now are heavily focussing on innovation, and future proofing (as much as possible) - the criteria for concrete for example is to last 100 years.
I think whilst they may not be going about it the right way, it is something the UK desperately needs, and I'm just comparing it to the experience I have had in the many European cities and countries I've visited.