We have engineered wood (floating over cement floor) throughout the ground floor and love it - it's easy to keep clean and looks fantastic. I've had a few hot oil splashes in the kitchen and it cleans up just fine. My husband fitted it (experienced DIYer) and he says it was easy and straightforward, he followed the same logic - you can rectify a disaster with floating floor, whereas once glued there is no going back. I've also noticed the floor contracting /expanding a tiny bit throughout the year which I'm not sure how would work out if it was glued down. The only thing I'd say is make sure you cement underfloor is as level as possible, and then level it out some more - we didn't bother too much and the floorboards do squeak in one place over a slightly uneven bit. We got the best insulation we found and I'd never noticed it being particularly cold. We are moving next year and having the same floor but with underfloor heating and no radiators - it'd be fabulous! Good luck on your project!

The only way you can be sure of which colour will work with your cabinets, is to see the actual tiles in the space. So if you can, get samples out and lay them on your floor against the cabinets. If you have to choose between those two, I'd go for the dark one, but that is just because I think that light grey is such a cold colour and it's hard to say if it works with your cabinet colour. The dark tiles will make the space darker though. If you can go for another option, I think Jules' idea of going for a wood look tile is better.

A family member has bought a house with a similar original layout that had been extended upstairs with a car port underneath with access to the garage. It works but the house is quite unbalanced and downstairs feels cramped so they are now looking to extend to rear to extend kitchen which will give them similar to what you are planning. Not what I would have done but they wanted to live in a particular village. I think extending is so expensive and risky at the moment that I would seriously consider if moving is an easier and cheaper way to achieve what you need.

Finish to the island would depend on the flooring and the overall look you’re going for. As for putting base cabinets on top of LVT ridged core - I don’t think it’s advised. Have you thought about base cabinets and then fit the flooring to just under the cabinets enough that when you put up the kick-board it looks like it goes under the cabinets!