Hard to say without knowing more about your tastes, budget, etc. but since you've posted in the "budget travel" forum I would assume that these aren't extremely extravagant.

If you were planning on eating in lower/mid-price restaurants and not doing an excessive amount of shopping I'd think 2000 GBP would be plenty. That's almost $150 per day and you can certainly survive in either city for less than that (of course, the shopping is a big wildcard as you could also blow much more than that in a couple of hours depending on what kind of shopping you are doing!)

If your accommodations are such that you'll have access to a kitchen and can cook some meals for yourself, then I'd say you definitely would have nothing to worry about.