It will depend on the cubic area of the bathroom, to the size of the extractor you will need, this will then determine the correct outlet size for duct out of wall. So even though you have hole it may not be correct size. You would require an overrun on the unit to.
The electrical as in a special location, will need to be notified to building controls either via direct application or by using an electrician that is registered with scheme provider under
competent persons.
If notify direct without use of competent person, the fee can be quite large and often can not justify the amount of work, so best using competent person, as far as cost is concerned.
So say your bathroom was 3 metres long X 3 metres wide and ceiling height was 2.4 metres.
You would need a 5 inch outlet hole for duct.
So material cost would be about
£20 for duct kit
£60 for extractor
£6 for three pole isolator
£1 per metre for three core and earth cable. account for 10 metres just as an example.
£5-10 for fixing, sleeve bits and bobs.
£5-10 for plaster (remedial work)
So material cost will be around the £90-100 mark.
Then labour on top of that, this will depend on location and accessibility to work area.
After coring new hole, chasing out, sinking boxes, mounting equipment and accessories, routing cable and termination, inspecting, testing and certs plus remedial work. Could end up being a three quarter day. expect to pay for a full days labour.
If you go
here you can calculate the performance needed by the extractor and also link you to suitable fans, but go for a timed/overrun type.