Actually, sterling has never recovered to its levels before "Leave" won the referendum:
http://www.xe.com/currencycharts/?from=GBP&to=USD&view=1Y
The pound was going up in the days before the referendum (when the markets thought "Remain" would win) and it tumbled almost 15% when "Leave" won. It's still 10% lower now than it was before the referendum.
Sorry, I was thinking of the stock market and stand corrected.