Short answer: fees vary widely from agent to agent.
Longer answer: It's not that hard to find private landlords in London. Use Gumtree and make sure the box marked "agency" is not ticked. Not every single agency charges (some use the fact that they charge no fees to tenants as an advertising mechanism), but the vast majority do. There's no hard & fast rule about the rates, but there are some notorious ones that charge much higher rates than average. Best thing is if you're interested in a property, find out straight away what their fees are BEFORE you fall in love with the place. Not all agents charge for everything, but most will charge you for: referencing (non-negotiable as this is out-sourced), admin fee (for drawing up the lease), and a check-in fee (for doing the inventory).