Hi Steve, Just done this on my car (birthday present in my case!).
On the standard Morgan mirror assembly the tube in mirror base, into which the mirror stem fits, is too large a diameter for the mirror stem. To stop the stem moving around (rattling) in the base, the bottom of the mirror stem has a grove machined in it. A grey plastic spacer collar, with a split in it, is fitted in the grove to take up any slack. So, when you undo the clamping screw on the mirror base to free the mirror stem you need to remove the locking screw fully, otherwise when you try to withdraw the mirror stem the grey plastic collar fouls on the clamping screw preventing you from withdrawing the mirrors.
The mirror stems on my new round mirrors (Phoenix Design type) are a larger diameter (see below) so don't need the grey split spacer collar when putting the new mirrors in place. I suspect most after market fitment mirrors stems will be of the same sort of diameter.
Also, when you do withdraw you existing mirrors, you should find two seals which fit round the mirror stem and over the top of the mirror base. One in grey plastic beneath another black one which you should be able to see with the existing mirrors in place. You will need to remove both these seals from the existing mirror stems and replace them on you new mirror stems. Because of the larger diameter of your new mirror stems, you will need to lubricate the seals/stems to get the seals on. I used a small amount of Fairy Liquid (other brands are available!) on both the mirror stems and the seals, but they weren't difficult to replace.
Finally, you can insert the new mirror stems (with both the grey and black seals positioned on the stems) into the mirror base, refit and tighten the clamping screw with the mirrors in your chosen position, and slide both the grey and black seals back into place.
Voila! Job done... Bon chance