There are very few circumstances in which an insurer can refuse Third Party liability. Section 148 of the Road Traffic Act, and an EU directive (which is harsher and which has been carried over into UK law) forbids them from doing so.
They may refuse liability for cover which is not required by law (e.g. damage to the policyholder's own vehicle) and they may try to recover their Third Party outlay from the insured if the terms of the policy have been broken. I've just had a glance through mine (taken out last April) and I cannot see any conditions which restrict my driving unless for an "authorised" purpose.
//I was on my way to food shop, "prove otherwise" ?//
Exactly. The listed reasons why you may travel (and the list is not exhaustive) is so varied that you would have to be a complete numpty to let anybody believe you were out of your home without "authorisation." For example, you can leave home for exercise. But it doesn't limit how far you can travel for that exercise. You could be driving to your favourite walking spot and still be "legal." You may even be going to your local optician in Barnard Castle. You are allowed to "...seek medical assistance, including to take any medical tests, be vaccinated or access any of the services referred to in paragraph 47 of the Schedule;" Paragraph 47 lists "Dental services, opticians, audiology services, chiropody, chiropractors, osteopaths and other medical or health services, including services relating to mental health."
I think Sky News is suffering a slow news day.