The train is a French TGV, these do not operate in the UK (not to date anyway) The Channel Tunnel passenger train is the Eurostar.
An early draft of the script was set to feature several characters from the original series all being killed off to raise the stakes for the new characters. The producers wanted to bring back as many of the original actors as possible. All declined, as they felt it was disrespectful to the original series. As a result, only the character of Jim Phelps was brought back, albeit as a surprise villain and not a hero.