Certified GKH Gardening Expert
This tree does not do well with moving. This is, especially, true when it is already established. It can be done, but I would seek the assistance of someone in your area that has experience moving existing Japanese maples, specifically.
I can offer another solution, however. Taking a cutting during dormancy (really several cuttings so that you can be sure that you get one tree to survive) can help you to move a smaller tree. You can opt to let it grow on its own, slower, root system, or graft it to a faster maple species as a root stock.
Here are some articles that will help:
Thank you for your very helpful advice - now need to find an Acer expert in the UK, preferably London area