The finished depth of insulation will be about ten inches.
The ceiling timbers will probably be about four inches, and they will (should) roll quilt between then to this depth. Then they will flop a big blanket over the top to make up the insulation depth
You can't put flooring on top of the blanket and squash it for two reasons.
However you can counterbatten the existing timbers by putting new timbers at right-angles to them, and the flooring on top of that. You will have to slice the blanket to fit the new timbers. The flooring should be slightly higher than the top of the insulation to give an air gap and reduce the risk of condensation.
Carpenters will not like doing it as lofts are horrible to work in (too hot or to cold, cramped, very dirty, and older/cheaper grades of insulation shed itchy fibres.
The flooring will not be strong enough to use as a habitable room.
An alternative more modern method is to insulate betwen the timbers, then lay rigid foam insulating slabs on top of it to make the depth, then put flooring on top. No battens are required as the rigid foam tranmits the load from the floor onto the timbers. You will not get this done on a grant as thre rigid boards are much more expensive. However a carpenter will probably not mind doing it so much as it is mostly sawing and screwing so not as dirty, and the board does not shed fibres. Kingspan and Celotex are the best-known brands. Yoiu might find a display in your DIY shed or builders merchant.
If you every buy rolls of insulation yourself, look at the packaging to see if it has the coating to prevent dust and fibres. the trade name is "Ecose" but there may be others. Some of it is branded Knauf. If you stroke a bit it feels sort of silky.
It is usually available with the energy subsidy and very cheap.