Here in Central London I grow melons in pots - or, to be more precise, in buckets, using compost mixed with pelleted chicken manure. Last year I grew Ogen and Galia, this year I'm going all out with Galia, Ogen, Edonis, Ananas, Minnesota Midget, and a couple of watermelon - Sugar Baby and Crimstar. All doing well in little pots at the moment, hardening off nicely (though I lost a few in the recent cold snap) and will be finally potted up this weekend.
Good luck!
;D