I was curious, so I plugged into the handy ITA matrix (which I plugged recently on another thread), a month-long search during October, LON-INN:
matrix.itasoftware.com
In October, the lowest fares are coming back at 222 pounds. Austrian, BMI, and Lufthansa all fly there. Star Alliance seems to be your friend to Innsbruck. As it gets closer, maybe there will be better fares.
Fares to Munich are much, much lower, from 80 pounds.
The train from Munich to Innsbruck is about 2 hours.
You can check connections at either the German site,
www.bahn.de, or the Austrian one,
www.bahn.at. I'm getting prices ranging from 58 Euros r/t (special fare, requires advance purchase and riding a specific train, no refunds) to fully refundable and changeable fares for 106 Euros r/t.
The trip to Innsbruck from Vienna is much longer.