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For a start, where are you staying? If you're keen to meet people, Couchsurfing could be the way to go - your host can often introduce you to friends and so on as well.
Alternatively, consider a hostel. Pick one with a good atmosphere rating on hostelbookers or hostelworld; and ideally one with a free breakfast and common room - that way you meet other traveller at breakfast or just chilling out in the common room, and it's often fairly easy to convince other travellers to go do something random or hang out together.
Drawing-wise, there are the groups like the London Life Drawing Society, if you're into that type of drawing, as well as the Centre for Drawing, in Wimbledon, and the Royal Drawing Society.
Pubs are also a great way to meet people, but it's easier (for me at least) to go with someone else to the pub, and then start chatting to others.
Pick up TNT Magazine - they are free and outside most tube stations, and look for events, comedy gigs and all sorts of activities in there - lots of expats (Aussies, Kiwis, South Africans, Canadians and more) doing various activities together - something in there may just catch your eye. The TimeOut magazine also has lots of events listed in it as well.