Since you allege the condition exists and would be covered under UK consumer law, you would likely have to collaborate that with some form of proof acceptable to the UK legal authority, and Apple, Inc.
If a third party did the diagnostic, using acceptable practices, tools, training, etc they'd be accountable to both Apple and the UK authority regarding consumer laws. Others have written in these discussion forums about issues covered under UK law, and some have provided a link to the official consumer law details.
So you likely have a plausible case to present; though there may be some extenuating circumstances; one such would be if there were damages not consistent with normal wear. Like a seismic fault-like crack across the case; or some condensate of oxide from dampened interior corrosion due to leaky beverage contents, etc. There usually are some pages of fine print that could be argued by legal experts, on both sides. In this country, they're usually not so pre-argued.
Anyway, hopefully it works out.
Good luck & happy computing! 🙂