When you first arrive in London the easiest option is to hook up with a friend (or a friend of a friend) and sleep on their couch for while you look for your own accommodation. Make sure you don’t overstay your welcome and pay £5-£10 a day towards household bills.
Hostels are great for short-term stays. Expect to pay £10-£25 a night depending on the size of the room and always ask about weekly rates, as there may be discounts available. Check out YHA hostels in London and the Generator Hostel in King’s Cross is also popular with travellers.