Will depend on all sorts of things. The type of birth you have, how long the labour, any health complications.
But in general, if you are physically well enough to be discharged then discharged you will be. This is very much my experience of the NHS all round. You do not get a choice.
With my first dc, delivered at 12 noon, postnatal ward at 2, starting asking about discharging myself by half four, discharged at 6pm. This was very much my choice and I could have stayed over night if I wished to.
My second dc was a home birth.