I have found the answer to my problem – it was caused by the banking security program TrusteerRapport, which has apparently caused problems with flash before, and which runs outside of the browser so the usual things of running without add-ons etc. doesn’t cover it. Anyway I stopped the program’s processes and the problem with the flash plugin had gone.
If you have TrusteerRapport on your computer then open Task Manager (as Administrator), then under processes click on each of the three Rapport entries and click end task for each. Then run Firefox and try it. Be aware that, unless you uninstall Trusteer, it will start up again if you do a restart, and you will have to repeat this step. I am about to send a report to Trusteer asking if they are aware of this and have it in hand.
If you don’t have Rapport, then perhaps a similar program which runs in the browser without being a plugin or extension may be to blame. Good luck!