Firstly if they ask at application, then they are looking at if there is a risk with you paying monthly, if you have a CCJ some brokers and companies will insist on full payment. These tend to be companies that have been stung before because they 'borrow' the full cos themselves then let you pay it off by instalment, if you default then they loose money, though tat tend not to ask at application tend to have in house insurance so dont have to borrow to buy in the insurance!
Secondly if you make a claim, they need to know as it can be an indicator of fraudulent activity, if a person has suddenly developed a few CCJs, then makes a weak claim on the insurance (first party as in fully comp) then they have to be sure it is not a 'fiddle', as these are adding huge amounts to our insurance each year. If it is just a third party claim, then they dont worry, it is only if you are claiming for yourself.
They also added that they will often not ask this UNLESS they thinks something is wrong with the claim whilst they assess it, obviously if you had fully comp and were hospitalised by an uninsured driver, then they will pay up and normally not ask, as that is a strong claim, but if your car is 'nicked' from the garage that you "may" not actually have because you live in a tower block, whilst it had £1K of sound system inside along with brand new alloy wheels, then they will class this as a weak claim so will fully investigate to avoid a fraudulent claim!
So there is another explanation, it is not about stopping you having insurance it s more about being sure there is no fraudulent aspect to a claim
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Abbreviations used in DQF
My advice is guidance only, if you want the law then consult a lawyer!
(c) All Spelling mistakes are my own design, infringement of them may result me sulking!