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Underneath the existing units are there tiles? Or is it just the subfloor (concrete).
You should be able to build the units on top of the subfloor and then have the plinth hide the unfinished floor, the only thing to consider is the height difference between current tiles and future floor covering (which might affect how short you trim your plinth and the height you set your units)
We're about to do our kitchen. We were originally going to replace the floor at the same time, but for the sake of costs might just live with the tiles that are currently in there. The kitchen is already on a concrete / level floor so should not need work under the tiles.
Does anyone know if it would possible to replace the tiles at a later date (in a few years perhaps) if the units are already there? Appreciate that it's likely harder and more expensive than doing it now, but for the sake of costs this year is it still a viable job to do?