Ok, so there was never any doubt that the floor tiles needed replacement (they're actually particle-board tiles, no longer available, but almost exactly like cork in appearance).
They were half rotten, no longer stuck down, warped and filthy. And it was immensely satisfying to pull them out and ditch them out. After I removed all the no-longer-stuck-down ones, we had to get a fair bit of help with the rest, but persevered and managed to remove them all:
...and then we went a bit further and took up the vinyl on the kitchen floor (see photo above) - "cork will be nicer" we thought gleefully and we ripped up the actually-not-that-bad vinyl.
Then we (well, the Eastern European boys) ground back the concrete, leaving it smooth and shiny like a baby's bum, ready for the cork tiles:
That's fine, we figured. It would look super. Then yesterday our very sheepish builder phoned. They weren't ready to go, they were actually at customs, and for some reason MAF had declared them unfit for entry. And destroyed the whole shipment. Another shipment isn't due til after Christmas. And we have no floor. Just smooth, smooth concrete. We're fucked.
I raced around - Bunnings, Mitre 10, Placemakers, the Flooring Centre... blah blah blah blah. Matt started looking at parquetry (even more expensive). We have had to abandon the 8mm thickness - 6mm is all that is in the country.
This morning I phoned Bunnings stores all around the country - they all have a few square metres - we need about 100. A lovely lady at the Auckland head office is going to try to collate them all together for me, our fingers are crossed that there's enough.