The good bits - easy purchase, arrived promptly, and the no-quibble returns went very smoothly, so this is still a recommendation for Backmarket.
Unfortunately the unit itself was terrible. It arrived badly packaged (rattling around with only a small air cushion on one side). To comply with the return i had to repackage it.
The unit was dirty, I cleaned part of it before even turning it on as it was kind of gross.
When turned on the fan was incredibly loud, like the volume of a hoover. This seems to be a common thing with early Pros and would require reapplying thermal paste and cleaning the unit out. This obviously hadn't been done despite the refurbishment claim.
Unit was shut down, and returned with no issues for a full refund. I highlighted these issues to Backmarkets customer support.
To be clear, I've purchased through Backmarket before for phones and other devices and this is the only time i've needed to return an item. I'll be happy to attempt to purchase another PS4 through this site soon.