Sorry, RAV 1D, but you are mistaken.
As I and other have explained many times on AB, uUnless it specifically says so in the Terms & conditions of the policy, having no Vehicle Excise Licence will NOT invalidate insurance. Even if such a term is included it will not apply to the compulsory “Third Party” element of the policy but only to any additional cover such as Fire, Theft or Accidental damage to the insured vehicle. Insurers are only allowed to void Third Party insurance in very limited circumstances such as when the driver is disqualified. Similarly lack of MoT will not affect compulsory insurance.
Note that MoT and Road Tax offences are usually dealt with by way of a fixed penalty. If lack of either of those two automatically invalidated the driver’s insurance and the police “wanted to be funny” by laying the far more serious charge of No Insurance I’m sure they would. But they don’t. You can also see this demonstrated by visiting your local Magistrates’ Court on traffic day. Here you will find drivers appearing charged with either no tax or no MoT who have for one reason or another not been dealt with by way of a fixed penalty. You will find that there too drivers are charged only with the Tax or MoT offence and they are not automatically charged with No Insurance as you suggest.