The vibration was due to a badly worn water pump and the reason that it was becoming more obvious at lower speeds was that the wear was getting worse.
So I now have a brand new water pump to go with all the other new bits but unfortunately the old fan belt pulley was too worn to fit properly on the shaft of my nice new water pump. Hopefully the pulley will arrive in time for it to be fitted before the weekend, as Murray would like to take me on the Epsom Area MG Owners Club run to the Bluebell Railway on Sunday. We shall see.
It will also be interesting to see if the new water pump also solves the persistent but small water leak that is still troubling Murray. John said that when he took the old pump off there was some evidence of leakage behind it, so fingers crossed.