Has it by chance got an electric fan? My Westfield used to run on until the fan stopped rotating as the fan was acting like a generator sufficient to charge the ignition. Isolated fan properly and no problem.
No, it won't be the electric fan. It'll be the usual Cooper 'S' running-on situation which has been happening since about 1963 when the 'S' was introduced. It is not an issue so long as you select 4th gear and let the clutch up as you switch off to completely stop the engine.
