Just as an update for everyone who had kindly helped with their advice...
The original "tiler" came out again and reckoned there were a few "snagging" issues but he could fix them and it wouldn't all need removing. He accepted he could have laid out a few bits better and was generally apologetic, but couldn't see that a lot of the things were really issues (e.g. wonky uneven could be fixed by "scraping it out with a nail" ).
I unsurprisingly wasn't interested or convinced, even though he assured me that he would would do whatever he needed to make it look good. We eventually agreed that we would just both walk away with no payment.
Happily
@Andy Allen happened to have two free days due to another job not being ready for him and he has managed to sort it all out wonderfully. What a difference! My wife is now over the moon with her kitchen.
The one good thing about the guy doing it badly is that, despite being up for a week, Andy managed to get most of the tiles off just by flicking them with a screwdriver as the adhesive still hadn't really set and crumbled under a bit of finger pressure. The guy also hadn't prepped at all so the underlying paint was coming off in sheets like paper.
Thanks again to you all for your advice and recommending Andy!