You'll be well catered for with Rugby at LSE, there are three men's teams and a women's team. i know nothing about rugby but the men's teams are supposedly not that great at it.... but who cares? they like a drink and a laugh and that's the main thing. women's rugby is really popular as well, they have about 30+ members, always a bit of rivalry between them and the LSE netball girls over who is the hotter etc...
as for football you couldn't go to a better uni in London for it. There are seven teams, all of which are some of the most successful at their level. the first team are near professional standard, they won the ULU Cup 2 seasons ago and play in BUSA and consistently do well in ULU Premier 1. the third team have won 2 successive promotions. Even at the bottom end of the spectrum the LSE seventh team are reknowned around campus for being pretty good - they play at the same level as other unis second and first teams so that shows you how high the quality is.
the football teams play at Fortress Berrylands, the LSE's sportsground in south london. away games are at the various university sportsgrounds around London - Imperial are based out near heathrow (bit of a trek that one), UCL at Shenley, where they share with Watford FC, and GKT medical school share with Chelsea at Cobham. You'll also have the pleasure of visiting such delightful haunts as Perivale (School of Pharmacy), Peckham (some GKT teams) and sometimes have to trek all the way out to Reading to play Holloway Women's Prison.
be warned though, the competition is for places on LSE football teams is tough - last year there were around 100 people who went to trials and didn't get on any team at all.