Hi, try www.rocketvan.co.uk they are based in Union Street SE1. My parents used them recently and were really impressed with the service, they have transit vans and charge by the hour, very reasonable rates.
Call "Friendly man with a van" Paul Dulake. Lovely guy, very clean van, very prompt,helpful and good rates.
I have moved three times with him and used him at work too for deliveries to clients-who now also use him! Enough said I think!