First off - pull the plugs and tell us what colour they are! If black or dark brown you are running too rich - which is a possible cause. Also check if the vacuum advance is working as it should - suck the pipe and watch to see if the plate inside the dizzy moves - this can be a cause of running 'retarded' and can lead to running on. If all ok - advance slightly until you get some pinking when working the engine hard in 4th gear, then retard it slightly until it is 'just not quite' pinking!! Another possible cause is poor quality petrol - may be worth trying a different brand.
The usual reason why an engine keeps on running when you turn off the ignition is because the mixture is too weak.
Try unscrewing the mixture adjusting nut at the bottom of the carb by one flat or two and seeing if it makes any difference.