Where you booked might be relevant. I know from experience that when you change the cities and your booking was with the AA RTW desk (and you call them to make the change), the AA rate desk only charges the difference in taxes. I recently changed my current itinerary, and the taxes on the new itinerary were lower. The difference consumed most of the change fee and I only had to pay USD $17.

Overall, I would guess that you don't have to pay the ex-England (or any) tax more than once, but you should def check. Why not call and ask? You'll obviously get a more definitive answer from an airline rate desk, and any answer you get here will be unhelpful, anyway.