This is a pet peeve of mine. It hurts not just the other cities in the UK, but London as well. We don't alleviate overcrowding in London by making it easier to move to London. We alleviate overcrowding in London by making more other locations economically stronger.
That should mean strengthening a region around Birmingham, faster links connecting the Leeds - Sheffield - Manchester triangle + tack on Liverpool, and a wide orbital around London improving connections between the towns around London that now are reduced to feeder/sleeper towns. There are towns around London that has decent direct rail tracks, but where the fastest rail route is a 2x-3x longer journey in to a London terminal and back out again. Actually run direct trains, and you suddenly have new viable commuter regions that bypass the centre.
Only after that should we think about making the links between these centres faster.
The problem of course is that many of these will need to be run at substantial losses for years before enough companies etc. will move/get established to change transport patterns, and it's so much easier to justify building more expensive routes where there is existing overcrowding.
Never mind that doing so just attracts more people.