You won't be taking the Trans-Mongolian from St. Petersburg - the train starts in Moscow!

It's a bit tough to give specific advice with the limited info you provide, and really you need to do some serious research and work out the options.

Some general thought:

1 - If you book the train part of the trip before departure you're a fool. You'll have no flexibility and any stops will be in theroetically-decent-but-in-reality-crap-and-overpriced hotels. Use an agency to get a Russian 'business' visa which means that you can simply roll up in Russia and have 30 (or whatever) days to do as you please (i.e. take the trains and stop where you see fit) with no need to have anything pre-booked. Both train tickets and hotels are easily sorted as you go.
2 - Research Mongolian visa options, about which I have no knowledge.
3 - For the outbound flight the ideal option would be QF/BA to LED with a LON stopover. How ideal the price will be is another question though.
4 - Flights SYD-LHR are pretty cheap.
5 - Options to get from London to Moscow to connect with the train are numerous. Flights to Russia are generally expensive , so consider flying to VNO (Vilnius), RIX (Riga) or TLL (Tallin) and then training it to Russia. HEL (Helsinki) is also a reasonable option for this. VNO, RIX, TLL and HEL all have trains to St. Petersburg as well.
6 - Chinese visas are easy to get - it's just a case fo filing in the form and taking a trip to the consulate.
7 - If you're in the mood for adventure extend the overland part of the trip to Singapore.
8 - OW tickets Asia-SYD are not a problem.