LennyW

Thanks for the advice everyone. In the end, I tiled down to the floor - which wasn't tiled - and put the skirting over it. It looks good, particularly (as Cooperman pointed out) this way, you retain the full profile of the skirting, the top of which was half way up the the bottom tile - pure luck. I would imagine if you got a horizontal grout line near to the the top of the skirting it wouldn't look so good.
I overcame the butting up to the door frame problem by making sure the architrave was of sufficient thickness.