Posted: 14/12/2016 at 17:31
Looks like a Cordyline from the pic but that is a pretty big plant to transplant.
Somerset is fairly mild at the moment - at least on the coast and if you have to move the plant now, you should have a few days to do it in.
The more I look at your pic, the more I'm tempted to say forget about the largest growth and concentrate on the smaller piece. If you are able to dig it up, you will need a planting hole to accommodate all the main root.
These plants are quite commonly offered for sale and it may well be better to just buy a new specimen to plant.