I prefer to transplant and move my plants from Oct - Dec when the rains will do most of the watering. Now is the time when there is growth in the roots and not much up top. At least for those of us who live in warmer areas. I like to us the equinox as the cut off date.

In the UK (where you aren't!) we are best moving evergreens after March, so it is a bit late now. why not check with a local nursery or garden club.