Thanks again for all your comments. They have been really helpful. Below is an update of our situation.
To recap the tiler came round and replaced some of the tiles with extreme lippage, at this time he said that with these tiles the finish we have would be as good as it can get, even if he started again therefore relaying the floor would not lead to a better finish. (And in response to Jay there was no self levelling compound laid.) Thus we went back to the shop, they said they are only responsible for supplying tiles and whilst they recommended the tiler they do not wish to get involved. However, they repeated these tiles would give us a floor which would be virtually flat (as it is a natural material it will never be totally flat due to the top layer), and they reiterated they were top quality calibrated tiles diamond cut on one side. This means there would be no trip hazards or protruding corners - which could be an issue as the bathroom will be used by young children with bare feet. As these opinions contradict (the fact that it would be virtually flat and we would always have a noticeable lippage) we insisted the shop and the tiler come round to our property to agree who is correct and the way forward. We have been promised they will be in touch on Monday and we will keep you posted.
(In response to NZ_Tiler he applied a sealant after the first visit. But when leaving after his second visit in which he did the repairs he felt necessary, said he would come again once the bath, sink etc had been plumbed in and reseal the whole floor again. I am assuming that the fact it hasn't been sealed explains the difference in grout colour between the two visits.)
As a final aside, we are attaching a picture of the original tile (the corner in question is the one immediately to the left of the triangular tile and by the corner with the arrows pointing to it) and that which replaced it. There seems to be a corner missing (the pen is to give an idea of scale) and we don't know whether or not to raise this as an issue, it doesn't look good to us, but we aren't tilers.
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