Try www.streetvan.co.uk - brilliant easy service, no connection but after numerous times renting vans from 1Van1 off Druid Street (now gone bust I think) and filling in long forms every time, this is a much better option.
In saying this I have not met more rude staff in my life but much cheaper than street van and open Sunday so weekend 24 hour hire is a possible. Perhaps they were bad with my but very abrupt and unhelpful.
sorry to but in so late after the event, but the cheapest of all quoted on here is the London Transit Van Centre (www.ltvc.co.uk), also on the Old Kent Road. They are helpful, the vans are immaculate AND they are cheapest than all of the other companies mentioned here. BTW, as seems to be forum etiquette, I should wish to confirm that I do not work for, own or have any family members involved with the LTVC; I just happened to use them a few years back.
However, I can second (or third) the other recommendations for the hire place up at the Borough (carpoint). To be honest, I would rather use either carpoinr ot LTVC rather than Streetvan or one of the 'larger' outfits.