Insurers have access to The Central Underwriting Exchange Database. It will tell them about any claims you have had with previous insurers, any convictions you have disclosed to previous insurers and any insurance fraud you or anyone in your household has committed. At present, we cannot access your driving licence details on that database. There are proposals for it to show this information, but the Data Protection Act is currently impeding any progress on that front.
However, although insurers cannot currently access your licence, they can ask you to send a copy of it at any time and if you do not comply, they can void your insurance for non co-operation. If they do see anything on there which hasn't been disclosed, they can void the insurance.
We also often get phone calls from the police when they have stopped motorists at the road side. They will do a spot check to see if they have disclosed convictions to us, and if they haven't, the police will then ask us if we would honour cover. If we choose to void the insurance, the police will seize the car at the road side, and could technically charge them with obtaining insurance by deception.
A small percentage of people who fail to disclose convictions are lucky that they never have a claim and have never been asked to provide a copy of their licence, but the majority of people get caught, and once you attempt to defraud one insurer, you will find that the other insurers will all know about it and will be reluctant to take you on.