London is very expensive. There are no cheap areas; only more or less expensive ones - though all depends on what you mean by cheap.
That said, budgetary issues aside there are many nice quiet areas. If you want to be close to the centre, yet not amongst the crowds, areas like Islington, Barnsbury, Canonbury are nice, with lovely quiet residential streets yet walking distance from busy areas with lots of cafes, shops, etc. This is in North London. If you want to go to south london and further away from the centre, nice quiet areas are places like Richmond and Kew.
I am sure other people will have other suggestions based on their own knowledge.
