The sewing machine is fixed (happy dance).
I was telling YorkshireLass about it and she suggested that if there was fluff under the bobbin casing that might be the issue.
I unscrewed the machine's throat plate with a dinky dwarf screwdriver took out the thing which houses the bobbin and it was full of fluff - the kind of fluff that has been there so long its almost felted. So I fished that out, discovering that it had a big knot of thread in it also, reassembled the bits and 'ta-da' it now sews again.
I would like to apologise to my lovely Janome for letting it get in a state like that and then expecting it to sew. I will try not to let it happen again and might even buy you some Gutterman thread as a celebration instead of making you sew with Moon thread.