sub-floor preperation

You may be better off using a latex levelling screed.

Hi Ralph, You can't float 6mm ply without fixings or adhesive it will warp. I have had to do this in the past, sounds like you need to make up 9mm in total? You can get a paint on chemical that works as a barrier, paint that strait onto the screed with a roller (usually 2 coats). Once that has dried Glue the ply down with wood floor adhesive. You should be able to find these products at a good flooring specialist.

Hi Ralph, I would personally lay the barrier first as this will protect the hardboard, then I would lay the hardboard not gluing or fixing just cut to fit nice you want it to expand and contract naturally so it doesn't push up the new floor. I would leave around 5mm gap around the edges of hardboard. This will help with expanding and contracting and would be covered by skirting boards. I hope this helps. Regards Craig.

f balls f75 liquid membrane,then latex self levelling is your best solution