My husband is in the Battalion following them around the world and as far as I know they are due to leave London in Summer Leave next year. They are due to go back to Cyprus I believe, but that is yet to be confirmed.
Remember it's only 2nd Battalion that's based in London at the moment. You could be posted to 1st Battalion in Paderborn if you join the regiment. If being in London is really important then look at the Household Division.