I think it will be a battle of the recessions, ie will Britain or the US go into a deeper recession?
The strength in the dollar seems to be because they reckon things will be worse in the UK and even more so, many still view the US dollar as the world reserve currency. I've heard that many emerging countries own loads of US dollars and to suddenly sell them would undermine the large US investment in their own countries and products. It would take a leap of faith to switch heavily over to some other currency.