We have never paid in sterling, but I can't imagine they wouldn't, it is business afterall. My husband is a cabbie here, and he excepts anything, but I have to say he does charge a little more to allow fx rates etc.
You could always check with your driver and worst case, if they won't go back in and and change some. Or, stop at exchange place on the way to your hotel and change some up to pay him. We used a exchange place just in front of the Silver Sands shack. Their rates were quite good.
Last year, they had changed their policy, so you had to take your passport, even to change up cash, but, they would take a copy and keep it on record, so they had it for future exchanges. This saved having to keep taking a passport out with us every time we changed money up.