Rather than make be campaign for another High Speed Line (HSL) in the UK the French experience makes me think it is the wrong answer to the wrong question.
The Train a Grande Vitesse (TGV), or high speed train, was a specific answer to a French question, and whilst it has proved the death knell of the domestic airlines between Paris and South of France (well over 60% of travellers travel by TGV) the UK is very different, more than anything else our methodology. Plans I have seen for the HS2 envisage city to city, and whilst many UK stations can accommodate high speed approaches these are invariably slowed as one hits 'commuter land'; travelling from Cheltenham Spa to Birmingham averages about 80 mph can be gained until the train passes Bromsgrove when the train tends to crawl from signal to signal; whilst a LGV would increase the journey, the final few miles would be crawling to stand on 'legacy' (well Victorian) alignments. The only way to circumnavigate this would be to build 'out of town' stations - which would add journey times into the town centre, or very expensive tunnelling. British Rail put forward an idea of tunnelling underneath Newcastle upon Tyne to provide a 'direct' through route to Scotland without traversing the legacy network, but was just too expensive.
As an aside the proposed HSL2 would terminate in some fashion in Birmingham, to get the full benefit you need a long route with few stops, which might be feasible is the route was to Scotland, but historically we are not very good at the 'Grande Projet' and the politicians would probably lose their bottle once it reached Birmingham, make it fairly pointless.
Getting back onto track, the other problem is the money; we live in austere times and when money is not an issue it is silly to blow £15 Billion or so one big project which will be paid for at the expense of the Provincial routes, and whilst the Felixstowe to Peterborough line might not be as sexy as a trains travelling at 185mph it is still needs to be funded. Again looking at the French model a HS2 would mean that services other than the old 'Intercity' routes would be downgraded, some eventually lost. Whilst I enjoy travelling on TGV services I am painfully aware that 'cross country' services are pitiful - one day, or a week in some cases - and the money spent on HS2 could be far more gainfully employed in doubling tracks, building new curves, separating the express from commuter trains at approaches into cities. Modest improvements could increase speeds significantly with change to spare.
Whilst train speeds should be increased, where practicable, it should be remembered the railway is a network, and whilst I have cited the French model the German model is far more appealing, a 'hub and spoke' network, and mixture of high speed services ICE, InterRegio, EuroCity along new and classic routes with strategic cut offs and junction. To be honest I have little faith in the UK going down the German.
Whilst High Speeds Lines are appropriate in the right circumstances I would rather the money be spent on getting the signalling right a Didcot than getting into Birmingham 20 minutes sooner!