I looked on the net for CarPoint but they seem to only buy and sell. I have looked at Thrifty they have good deal's and also Sixt.com (they are based in Vauxhall) but are cheap aswel. I will keep looking and let you know if I find anything else.
have you tried Sixt (www.e-sixt.com), in Vauxhall - they do Smart cars for £5 a day (haven't tried them yet but am thinking of doing so). Car Point on the corner of Borough Road will probably be a bit pricey for the bank holiday weekend. There is also a Thrifty on Tower Bridge Road, who are reasonable, or Easyrentacar in St Catherine's Dock but their prices go up closer to the rental period so will probably be fairly expensive now for the bank holiday, though still cheaper than Car Point I would think.
We've used carpoint too - very, very reasonable, and the guy there is lovely - I have to visit my grandmother in chesterfield every second weekend, which entails an awful trail up the m1, and regular traffic jams - he once waited for me until 7.45pm, and then didn't charge me a penny extra!!!! You don't get customer service like that too often in this village.