Since, whatever I did at this point, I was going to be at least an hour late, I elected to go back inside, make a coffee, do some WFH and email my boss to apprise her of the situation.
Because my boss is lovely, she came back with 'no problem, the important thing is making your bike safe'. So I worked from home for the rest of the day, visiting my friendly local workshop after lunch to have a piece of flint dug out from my tyre and a mushroom patch inserted.
Second puncture in under three weeks. That had better be the lot.