Should he...absolutely. It's not his country, he's just some unelected (as PM) (insert your own expletive). Unless he has gained explicit approval to do so from the CAA before-hand; he should know better than to ask. If the captain refuses, what's the worst that can happen? Error of judgement, but no transgression of the rules.
Now, had we a credible strategic VVIP outfit in the military, them's different rules, but let's not get started on that. After all, we're the only G8 nation not to have one....