No, completely false. All vehicles on the road must have insurance as required under the Road Traffic Act 1988, which is to protect you in the event that you injure another party. An insurer cannot suddenly advise they are no longer providing cover due to your journey not being essential. When taking out a policy, insurers ask questions like, "Will you require insurance cover to and from a place of work?". If you answer no, they can write that as an exclusion within the policy and use it to deny coverage in the event of a claim. Unless it is specifically excluded, they cannot then deny a claim.