Hi Hank,
It sounds like a great idea for a trip. However, be warned: Russian bureaucracy might derail your plans before you even get near a train.
I took the Trans-Siberian in February/March of this year. I am also a Brit, and had slowly made my way to Helsinki overland from my front door ready to pop into a Russian embassy and pick up a lovely new visa.
What I didn't realise that a few weeks/months previous, Russia
changed the rules so that the only way for citizens of nations outside of the Schengen program to apply for a visa was to do so
in their country of residence.
I tried all the options possible in both Finland and Estonia, yet no-one was willing to give me that piece of paper. Tail between my legs, I had to score a cheap return flight via London, stay a night and get an express visa issued. This enabled me to take the Trans-Siberian, and what an incredible experience it was, and I'd heartily recommend it. But if the situation is still as it was earlier this year, it looks as if your options for getting a Russian visa are severely limited.
I'd suggest having a good old dig around to see if those rules still apply - perhaps the
Russian Embassy London site is a good place to start. You may be able to courier them your passport and get a visa issued that way - it's worth exploring if you are really keen to travel into Russia.
Sorry to potentially p1$$ on your bonfire - but if it doesn't turn out to be a go-er this time around, do make sure you take the Trans-Siberian on your next trip, as it's an incredible journey through a fascinating country.