this is incorrect i think as this is BS 5385 7.1.9.2 Across joints
There should be no appreciable difference in level across joints
(commonly called “lipping”) and the maximum deviation between
tile surfaces either side of a joint, including movement joints, should
be as follows.
a) Joints less than 6 mm wide, 1 mm.
b) Joints 6 mm or more wide, 2 mm.
The above is correct across joints, this is where I got confused and please don't be offended by my understanding. What TTA are referring to here is tolerance allowed as you look down on the tile. Therefore if the joint is less than 6mm the maximum deviation in alignment as you look down on the tile is 1mm. Effectively if you had just laid the tile so it was still moveable, you could actually put your hand on it and twist it 1mm out of line and this would be within tolerance. This has nothing to do with the surface height of the tile against another tile. Believe me the amount of time I have spent on this is unbelieveable, even looking at regulations from the US and Australia for comparison.
The Australians have the best way of gauging lippage, they advise that by using a straight metal edge ruler from one tile to the next or protruding tile, if it allows a 2mmdrill bit to pass under it on the adjoining tile, this would constitute a rectifable defect. If the drill won’t pass under the ruler, the work is within tolerance.