The bike shop replaced both tubes.
While I was picking it up, I took the opportunity to ask what sort of bike I own (seemed like something I should know).
It turns out to be a 26" Mountain Bike - so there we are. And it's red.
It's definitely got three gears at the front, and 6 or 8 or something at the back, so it's somewhere between an 18 and 24 speed depending on the count.
I rode to and from work a couple of times.
My biking friends at work said how unlucky I had been to get a flat tire - 'that never happens on Mountain Bikes round town', 'I haven't had an MTB puncture in over 2 years, even on tracks', etc etc.
The next morning, the rear tire was flat.
I loaded it into the ever reliable Jazz (never had a puncture), and took it the bike shop where we had a terse conversation.