Conclusion
I'm pretty sure that this is a weird Opera bug. However, it's one that had me pulling my hair out for a while.
Just to really cause confusion, moving the off screen links inside the enclosing container div on a short page (like this one) stops the A key from working at all without using the Q key first!
Now is this behaviour particular to a given build/version of Opera?
For now, I'm off to have a nice calming cup of tea and a lie down!