Sterling will be more attractive because you can earn higher interest on it, therefore the pound will be worth more and you can buy more $ to the �.
However, the markets know that the BoE will increase the rate this week so its already priced in - that's one reason why you can get $2 for the � these days. If they don't raise rates (unlikely) then you might get less $ for your � but if they do then things won't change much