Any electrical work carried out in bathrooms must have a certificate of conformity, however I don't know if this is required if the unit is replaced with an identical model. I believe anyone can do the work, so long as an approved inspector passes it off and issues a certificate.
If it's a rental property, you would be mad not to adopt a belts and braces approach even if this is not a legal requirement.
You need to check with someone who knows the law and it is your local council that administers these certificates, so i'd give them a call.
Several years ago I carried out this task at home and I have installed a couple of these in my time. It's not hard if you comply with the installation instructions and fit an adequate supply back to the consumer unit, but then i'm someone with 25 years engineering experience, have refurbed several properties and have some relevant electrical qualifications.
As your unit is a straight swap like mine was, assuming the unit has been set on the tiling rather than in it, the job will be completed comfortably in less than an hour. The Triton T80 i fftted was £90 then, They have gone up a bit since. I reckon you should be able to get this done for around £200-250.