Does not "closed shop" relate exclusively to employment and, specifically, to the instance that employes are members of a certain Trades Union (as you say, now illegal in UK).
I'm certainly no lawyer, but I would have doubted that - since I agree with you when you immediately go on to say ...
As you say, any of that would be reasonable, but aren't you essentially saying that they are ('within reason') free to include whatever requirements/restrictions in their contracts/polices as they see fit - provided, I imagine, that they don't fall foul of legislation by decimating on the basis of race, sex, age, religion etc.?
One would imagine so - and the obviously could, if they so wished, be explicit in asking for just that. As was suggested early on, it's possible that they thought that being a NICIEC member was the only way of demonstrated adequate qualifications and insurance, isn't it?
Kind Regards, John