When I first moved to London 2 1/2 years ago I stayed as a long termer in a hostel for 3 months while I got myself set up. If you can handle living in a dorm I'd recommend it, the other long termers staying there were like a family and I made plenty of great friends.
Not all hostels will allow long term stay, however where I was staying (the Astor Kensington, now sadly shut down) it was not an issue, some of my friends were there for a year plus. There was also specific dorm rooms set aside for us so we wouldn't usually have random travellers coming through and making noise in the early hours of the morning when they left to catch flights.
If you are looking to save money while you look for a job plenty of places will put you on the payroll so to speak, you do x amount of hours around the hostel for free accommodation and a bit of spending money.
To give you an idea of what you can get I was paying 110 pounds a week for a bunk in a 10 person dorm room. Living in a room with that amount of people for an extended period isn't for everyone, but I had an amazing time and would wholly recommend it.