Sorry for some slight duplication in this story, but it is more specific to London to Bristol:
Christopher Irwin, chairman of the public transport passenger watchdog group TravelWatch South West, said: "We are looking at this with great interest as it has great potential. Trains on the Paddington to Bristol line currently have a maximum speed of 125mph and the quickest time between London and Bristol is one hour, 40 minutes.
"Faster trains would cut that to 40 or 45 minutes."
Mr Irwin said a lot of work had been done previously by Network Rail to look at high speed routes, including London to the West Country.
Transport operator First Group had also set up a working party, of which Mr Irwin was a member, to consider high speed routes, but it ceased after a number of meetings.
See
http://thisisbristol.co.uk/displayNode.jsp?nodeId=144913&command=displayContent&sourceNode=231190&home=yes&more_nodeId1=144922&contentPK=20928862