Are other people having issues with insuring their mini (or similar)?

As cost-of-living prices rise and a limited pension creates a squeeze, I have been considering getting "third party property insurance" rather than full comprehensive insurance for my minis, plus a trusty, loyal, old 1990s Camry that the whole family use in emergencies - mostly when their own car is low on fuel.

The Camry wasn't a problem getting third party insurance but no-one so far has shown interest in the minis.
Shannon's took my money for comprehensive insurance for many years but said they don't do Third party insurance at all.

NRMA don't want to know unless its full value comprehensive; Budget Direct, Enthusiasts and Over50s are the same. No-one has said why they don't want to cover the car but don't say why.

Any experiences along these lines would be interesting - especially from someone who can recommend an insurer.

PM sent

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1970 Mk2 Cooper S under restoration

I looked at 3rd party fire and theft on my 97 Cherokee, it wasn't much cheaper than comprehensive. With Woolworths insurance on it and our 2009 Fiesta for 3 years now.
10% shopping discount x2 every month is handy too.
I've had 1 windscreen claim on the Jeep and they paid it.

The MiniMatic on historic rego is still with Shannons.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

Just been declined insurance by GIO. At least the operator said they don't insure third party property vehicles made before 1976, unless they are renewal policies.

So the only insurance available to me and others in a similar situation, is fully comprehensive, despite the recent addition of third party property being promoted in advertisements for some well-promoted brands.
Thanks for your replies.