Having insurance cancelled, voided, or declined at some time raises a red flag for insurance companies. However the reasons for this happening may vary from the fairly trivial, to the extremely serious.
Unfortunately many automated quotes systems, such as on price comparison sites, automatically reject any application from someone in this situation.
It could be that in the past you have had a monthly paid policy; but you have run into financial difficulties and failed to make the agreed payments. Under these circumstances the insurer concerned would have been perfectly within their rights to cancel the policy forthwith.
You may have forgotten about a minor bump that you had several years ago, and not disclosed it on a proposal form.
On the other hand you may have (which we are sure you have not) acted fraudulently, racked up a huge number of claims in a short space of time or had been convicted of, or charged with, serious motoring offences.
Somewhere in the middle is the large number of people who have had blackbox (Telematic) policies but have had their insurance withdrawn under the 'three strikes and you are out' rules.
Clearly, with such a wide gap between those who have been refused for minor matters and those whose reasons were more serious, it is illogical that they should all be tarred with the same brush, but this is what can happen with an automated quoting system.
It is vital however, that no matter how trivial you feel the reason for your policy withdrawal was, that you inform any prospective insurer about it. They will find out sooner or later anyway. And if you haven't told them they will not be happy about it and cancel their policy too.
This is where talking to the insurance companies directly may be the only way of getting a policy at a reasonable cost, or even a policy at all. A specialist broker can be a considerable help in this respect.