Apart from the fact those lines are all electrified, the problem on the London-Brighton stretch is not so much train speed as it is line capacity and reliability.
South of East Croydon a substantial stretch is just double track (one in each direction), though most of the line has four tracks (which still makes for a massive chokepoint if a train fails) , and many of the stations have very few platforms and no extra track for trains to pass on. North of East Croydon, there's massive capacity problems on the approach to London Bridge, and on the path from London Bridge in to Charing Cross.
The result is that the slightest little impact to the time table at half a dozen points or more along the line have carry on effects along the entire line.
Increasing the speed of the trains would be great, but without upgrading capacity the slightest little problem would force a lot of following trains to slow down anyway.
EDIT: Apparently the "third rail" is also a problem for increasing speeds.
South of East Croydon a substantial stretch is just double track (one in each direction), though most of the line has four tracks (which still makes for a massive chokepoint if a train fails) , and many of the stations have very few platforms and no extra track for trains to pass on. North of East Croydon, there's massive capacity problems on the approach to London Bridge, and on the path from London Bridge in to Charing Cross.
The result is that the slightest little impact to the time table at half a dozen points or more along the line have carry on effects along the entire line.
Increasing the speed of the trains would be great, but without upgrading capacity the slightest little problem would force a lot of following trains to slow down anyway.
EDIT: Apparently the "third rail" is also a problem for increasing speeds.