I've taken a look at the government's proposals for rail between London and Birmingham (link).
1st claim: Journey time from London to Birmingham City Centre cut by over 30mins to 49 minutes.
I find this hard to believe. London to Birmingham is, as the crow-flies around 100 miles. This suggests an average speed of 122 mph.
TGV-Est, the fastest TGV service does Paris to Strasbourg direct in 2h19. That's 300 miles. That's an average speed of 129mph.
Before it sounds like it's easily achievable, it has to be remembered that Paris to Strasbourg is 3 times longer, so the urban distance (when you can't go at thundering TGV speed) is a lot more of the journey. You're probably looking at 10 miles at low speed (and then you've got to accelerate).
It's why TGV works so well in France - the distances to major cities are huge, so benefits are good (also, French trains before the TGV ran at dismal speeds - the effect of the TGV was huge on journey times).