To be fair, your average copper in the UK is liable to be sensible and sympathetic to any situation. As with the society from which they are recruited, there will be chumps and no point winding them up if you meet one.
If I get stopped while out and about in the current emergency I'll happily tell them who I am, and the reason for my excursion under the current guidelines in the broadest of terms, but they're not entitled to more than that and I won't be giving them more than that. Most coppers will be fine with that if you're polite about it - they know they can't start questioning people when not under caution and without their free and independent legal advice, so be cool, give them what they need to know and no more, and everyone is happy. They're just doing a job under difficult circumstances with poor strategic guidance and leadership, so it's a balance between your rights and their need to do a proper job.
"I am Bernard Aloysius Farquhar, BN 06/01/1969, of 69 Cleo Lane, Poshville, and I am on a journey to collect essential supplies/going to work as I cannot reasonably work from home/taking my daily exercise in public/travelling to assist a vulnerable person/travelling to seek medical treatment" is all you need to tell them (use your own name and DoB though, not mine).
BTW, a constable in unfiorm has the power to require a driver to stop in order to check their documents, if they believe they are committing a moving traffic offence, if they believe the driver of the occupant is 'wanted' or committing an arrestable offence - there is no power to require a driver to stop to chat about coronavirus related matters, although a couple of farces are doing just that. It my be they're asking these drivers for their documents to legitimise it, and then saying "oh, and by the way, why are you....?"
PS - sorry for taking it topically of topic there.
