Greetings Mr Lightning!
For your one stop, invaluable guide to transport around London, I reccommend
this website. It contains all the information you're likely to require about tube, trains, busses, trams and things. But not badgers

For detailed train information
National Rail is the way to go.
Which station at Mitcham are you closest to?
From having a brief look, take a train from Mitcham Junction to Balham (on the Northern line) then Clapham Common is a couple of stops away on a northbound tube. The train fare from Mitcham to Balham seems to be £2.20 return and the tube I *think* seems to be costing around £4.20 return. But of course, if you have a travel card, then the fares are obsolete and as long as your card covers zones 1-4 you're going to be covered.
I'll PM my phone number to you, so if you need me to help anymore, just give me a yell
