It's hardly direct is it though?
With regards to a connection / station for Heathrow, there is a provision for a station around Old Oak Common for a connection to Crossrail, which will connect to Heathrow.
I agree we need more London orbital infrastructure, not sure if rail would be the best way though.
What I think is needed is a sort of M25 for rail, connecting all the major towns around London. This would save a huge amount of time for people who have to travel in and out of London, reduce crowing in central London and provide greater transport routes for many meaning reduced car travel. if HS2 connected at this, say at Aylesbury, then the line would be of benefit to Amersham. Will it ever happen?
You don't say that your M25 rail should be high speed, but I'll make the following point anyway; HS rail relies on maintaining high speeds for long periods of time, so the more stations you put on a line, the less high speed it becomes. You can mitigate it to an extent if you're prepared to submit your passengers to sports car acceleration and braking, which can be made quite efficient thanks to Kinetic Energy Recovery systems, but I'd suggest that it's not the sort of handling a train customer likes.