Using a later shell that was in good nick at a time when Minis were worth £50-2500 was a viable and practical solution and this happened a lot especially if you had tipped a load of money in to all the nice goodies on to your car to find the shell was beyond saving come MOT time.
There was also an element of satisfaction in transferring your old bits over.
Equally I knew enthusiastic people who bought a brand new Mk3 or Mk4 shell for a grand or so at a time when the MK1 was a worthless piece of ... and instantly had a rust free Mini which they were very proud of. At that time most people applauded this 'upgrade'.
Conversely I know people who have bought a Mk1 that was re-shelled in to a new Mk4 shell in the 90's and since reverted back to a 'better replacement' Mk1 shell.
Right now if you had a 1983 Mini it would be tax, MOT and ULEZ free as that would now be 40 years old.
For a long time Mk1 shells were not available to buy and I would imagine of all the 'original' Mk1's around a very large proportion of the panels are replacements from Heritage or Magnum i.e complete floors, boot floors, inner wings, rear quarters, doors etc so very little is left of the original car.
The same applies to the vast majority of the running gear and trim. These cars often just used to 'evolve'
Times have changed as Mini values have increased but not every Mini with a new or replacement shell is owned by a criminal. Sometimes its just whatever is convenient or the owner had to hand especially if you are not a purist. Had it been a Mk1 shell of sorts from an entirely different car I bet nobody would bother commenting (unless the seta belt mountings were too high

The advert reads well and the guy is pretty clear in what it is and what it isn't.
As for ULEZ charges, a lot of people are either removing their modern car number plates altogether or fitting a licence plate 'sock' to avoid detection. I drove down a whole street in Enfield recently and witnessed this first hand. The police say they physically cannot keep up with the admin side of 'nicking' people and invariably let it go.