Have a look at Marlin serviced apartments. Available in different sizes at various prices.
Having used a few of them, I'd recommend the ones at Borough as its a few minutes walk from tube, there's a Tesco right next door, and there's a good gym on site.
Try tower bridge apartments. We stayed there for a couple of nights for about 250 in October. As the name suggests its right by tower bridge on the south side and y they did have a kitchenette.