The floor undernearth is concrete. Half the tiles are still on which will
need removing. I dont mind spending on it as long as the floor becomes
unsticky.

One point is whether you're buying the house, or letting it. If buying,
you'll be more bothered about a long-term solution.

Most of the solutions suggested so far make it clear that this is a
horrible (possibly dangerous) business.

Personally I'd never even attempt to remove the stickiness with
solvents: you'd be on for hours if not days, and you would never be 100%
successful. And you'd make yourself ill.

I would rip 'em all up (another poster has suggested ways and means).
Then I'd get some of that heavy duty paper that floorers and carpeters
use to underlay the underlay (very thick paper in very wide rolls). And
then I'd lay a nice cushioned vinyl on top of it all, and forget it.

And if I had a *little* bit more money, I'd get the shop where I bought
the vinyl to lay it for me, because they'd do it a lot better than me,
and a hell of a lot quicker.

hth
john