New petrol cap
So with a carb rebuild not solving the issue, I noticed when I filled up (the first time since the issue in Southampton) there was a gasp of air from the cap when it was removed.
In the hope that a failed cap vent was the culprit - the pump would have been fighting the vacuum it was creating when pushing the car - I fitted a replacement. Turns out this was another dead-end, so I'd have to look elsewhere.