I would not recommend a solid floor, with a height of 0.8m above ground level I doubt whether a cavity wall would withstand the sideways pressure.
The easiest solution would probably be to use concrete beams with a floor screed (and insulation if you want it) leaving a cavity below.
Assuming the new will be larger than the old and outside it the existing floor and walls can be used for infill. If the existing walls are to be utilised you will need to tooth or corbel them back and build the new walls from there. The top of the cavity wall can be closed with bricks with a vertical dpc.
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