I've seen this reported twice. It is nonsense & appears to have been pushed to the media to discourage ppl from driving. In short, absent the commission of other offences, driving in any circumstances is almost certainly covered. https://news.sky.com/story/coronavirus-motorists-told-insurance-might-be-invalid-for-non-essential-trips-during-lockdown-12128401

First, the new lockdown 'No. 4' Regulations impose no restrictions on a person from driving.

Secondly, the list of 'reasonable excuses' for being outside 'the place where [you] live' is inclusive not exclusive&includes exercise and recreation with no geographical restriction on where that may be. There is no mention of 'essential' save in respect of shops that may open.

Thirdly, whatever the government's guidance may say, it has no legal force.

Finally, it is right to say that the limitations of an insurance policy depend on the policy. I therefore looked at sample terms and conditions from AXA, which you can download here: https://www.axa.co.uk/car-insurance/policy-details/

This policy *does* have an exclusion for 'any liability, loss, damage, cost or expense caused by, resulting from
or in connection with your or a named drivers criminal or illegal act,...

...in circumstances where the convicted offence is one where the court has the power to impose a sentence of imprisonment.' (General Exclusions, para 15, p 31)

None of the regulations impose a sentence of imprisonment - they cannot as health protection regulations under the Public Health Act 1984 may not do so.

Thus, even if it could be established that a person was outside the place where they lived without a reasonable excuse, they would not be excluded under the terms of this policy. Other policies are likely to be similar.

While it is always advisable to check insurance policies, this appears to me to be a scare story intended to put people off driving. The irresponsible comments by those who should know better in this and other reports are nothing more than that.