Toby - don't float the wooden floors - floating usually means laying the wood on a vapour barrier (ie thin foam sheeting) and nailing / gluing to concrete floor. Laying on plywood means nailing / glueing a 2cm think sheet of ply to the floor and then laying the wooden floor on the ply.
A solid wooden floor floated over concrete, particularly new concrete, will warp and crack eventually as the concrete drys out and the boards shift. Floors laid on a ply base will not warp as easily as there is more flexibility in the ply to move and adjust to the changes in moisture and temperature.
I have had wooden floors floated and laid on ply, exact same board from the same manufacturer and both in new builds - the boards which were floated over concrete started to warp after two years whereas the boards laid on ply have been perfect.