Yes, that would work, landroverroy. However, I'd then have to look at the inner workings of the ball cock mechanism (Yes I know they will Cuddles, but I can't think of another way to say it!).
I guess the alternative would be to demolish the wall and re-build it. If that sounds a little bit drastic, let's all remember that PK moved house just to get away from his errant toilet seat!!