How often do nurses change their uniform in hospital ?

After each pillow fight pretty much.

--  Nurses are usually supplied by the hospital with several uniforms and the nurse changes her uniforms every day. Some may wear the uniform to work while others change in the hospital.

--  Depending in the ward and type of job, scrubs may be issued as well. Some scrubs are issued as part of normal work, and therefore washed at home by the nurse. Other "general" scrubs are washed by the hospital's laundry service, whether internally or outsourced to a private company.

Some hospitals provide scrubs for their nursing staff, others do not. But i'm sure they all have a supply of extra scrubs in case someone needs a change of clothes during the day.  

I buy my own scrubs because the ones they have at the hospital are all the same colour and the pants are either too tight or too loose.  I washed them every day when i was wearing them (current job nurse educator, i get to wear street clothes to work now).  Scrubs get very dirty after 12 hours, they get washed every single day

A nurse owns owns multiple uniforms and wears a clean one each shift.

Depending on their job, they may change in the middle of the shift.

This is not different in a UK private hospital vs a UK universal care hospital.