Thanks a million for all the helpful replies.
It does indeed appear that most spirit levels including mine will work upside down.
I've done a quick survey on the floor itself and on the ceiling below and have established that there is indeed some differernces in levels between adjacent joists but not so much along joists. If we start from the heighest point in the room, then a perfectly level floor would give about a 1/2" to 3/4" step up into the bathroom I don't think this is excessive but I gather the tiler laid the floor with the intention of minimising this. The problem is that this results in a
*noticable* slope across the floor and across the threshold.. We would much prefer to have a slightly larger step and a level (or not noticably unlevel) floor. As far as I undersatnd it, if a choice was to be made on how to lay the floor then it was us the customers who should have made it - not the tiler. And it's he that should bear the cost of relaying it to our wishes.
It might all sound like a fuss about nothing, but the whole point of paying an arm and a leg to re-fit the bathroom is to achieve something that looks good - you won't actually be able to do anything in there that you couldn't do before. In a bathroom dominated by large ceramic wall and floor tiles, squareness is everything.
Thanks again Jeff