Removing plastic / vinyl floor tiles

[Brannan]

I am in the process of fitting a new kitchen and I want to lay new floor tiles. The floor is concrete and it already has what looks like plastic or vinyl tiles laid. They look around circa 1980 something. They are very thin but boy are they stuck down good. When I try and remove them they either split into tiny brittle pieces or I end up taking a lump of the concrete base with them. I have got on no better with a hot air gun. At this rate it will take months to shift it all and then I would probably be left with a large uneven pock marked base which I would then have to level. Is there an easier way to get them up or would it be possible to lay new tiles straight on top as the old floor is already dead level and very solid? That would save me so much time. If overlaying is possible whats the best adhesive? Any advice gratefully received. Cheers.