Presuming there are 2 flats per floor you can treat this as a small building and use the internal doors of the flat to create the required 2 door protection to the stair, and also meet the requirements for a flat over 4.5m above ground level.
Hence the internal doors to the flat should be fire doors. I haven't dealt with non domestic since the new edition of part B part so I think (please check) that the doors will have to be FD20 doors i.e. a 30 minute fire door without a smoke seal or intumescent strip, and may not under the new regs require a self closer (previously it would have!) The front door should be a full 30 minute door including letter box etc..
Having said all that if you have Building Regulations permission for the conversion to 6 flats then there is no legal obligation to carry out the upgrade, but maybe aa moral one when selling!!
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