I, too, went to Traffords when starting my PPL training. This was only after an innocent comment regarding purpose of visit to the US was flagged by an astute representative at Barclaycard - their travel insurance didn't cover air related incidents/accidents and medical cover.
The only time any aspect of insurance arose was before the solo PPL training happened and I was offered the hull loss excess waiver. Subject to conditions this was and is always accepted.
My point here is more an ethical one. Take it right down to a tourist going for a jolly; if there is an incident/accident, should the tourist be liable for their medical care or become third party collateral and therefore covered by the FBO/FTO's insurance?
You can argue caveat emptor in a mom'n'pop outfit in the midwest, but as a flight student you are restricted to available providers by a regulator - the CAA.
The CAA is a monopoly service provider to the UK citizen. There is a covenant; we adhere to the regulations, they provide a service. Part of this service should include the FTO has a degree of insurance that covers the pax. You are not, after all, PIC.
I am not for one moment suggesting the CAA provides this cover, just that it monitors its training providers.
If the FTO doesn't have this insurance and the full cover details available on all advertising, they shouldn't have the CAA seal of approval. Period.