What do they mean by 'very uncommon'; that implies that it's not unheard of rather than 'not happened before'.
Unfortunately, not having owned it from new and being the only driver it is going to be difficult to disprove any allegations/suggestions of ill-treatment (not that it's easy if owned from new).
Are you able to contact the previous owner and do you know whether privately owned, company owned, ex-hire car, ex-MB press/demonstration car, as clearly only they can 'prove' not mistreated before you owned it. I would be looking to the selling dealer for redress; if they sort it via MB warranty fine, if not, they adress a different way.
I sympathise with the OP but have a feeling that this isn't going to be resolved easily overnight. The dealer (MB) is also in a difficult position; they were not invol@ved in selling the car (nor, presumably, servicing it) so if MBUK tell them it's not covered by warranty, they are also in an awkward situation as the OP isn't their 'customer'. Ultimately, the issue is back with the selling dealer, although I have had discussions with one 'specialist' dealer whose view, in my opinion, was that the remainder of the manufacturer's warranty effectivelty let them off the hook as far as any warranty was concerned.
I haven't researched the issue but are there other examples of reported similar failures that could help build a case? Having said that, it's the first I've heard of but that means nothing.