Bunged some air in the tyre last night to move the car to somewhere flat, and figured I'd take the opportunity to inspect the tyre as best I could.
So
Car moved to flat sideroad
Handbrake off
Engine on (so I could leave the lights on in case anyone drove past) in neutral
Get down behind the car with a torch so I can see the four inches or so of tyre visible, because the thing is so low.
Inspect tread width with torch,
Roll car forward six inches
Inspect tread width with torch,
Roll car forward six inches
Inspect tread width with torch,
Roll car forward six inches
Repeat till rotated.
Not a hint of anything in the tyre. At all.
I did notice, when inflating it, that the valve felt a bit loose (it spun as I put screwed the compressor pipe onto it - pretty sure it shouldn't do that...

) - so I think I'll be having a chat with the tyre fitter about that.
Anyone familiar with tyre fitting and know how the valve stems are fitted? I could google it but that way I'm sure madness lies.