Another one that comes in through search, and the answer is different from the house answer in two ways.
The permitted development rights that cover an air source unit on a house do not extend to a flat in the same way, so the planning half is more likely to need an application rather than less. That is worth checking with your own council before anybody quotes you.
The other half is nothing to do with planning. A leaseholder usually needs the freeholder's consent to fix anything to the structure or to the outside wall, and an external unit is both. That consent is a separate question from planning permission, it is decided by your lease rather than by the council, and it is the one that most often stops a job that was otherwise fine.
If anybody here has been through it on a leasehold flat, what the freeholder actually asked for would be useful to know.