I'll be moving home in June and I would like to take my cherry tree with me. What's the best way to do it?
I'm in the UK.
Here is a picture of my tree last summer.
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I like Ecnerwal's suggestion to leave the cherry in place. A gift to the soil and the new tenant.
If it must be moved, follow standard nursery practice and "ball it up" while still dormant.
During the late winter months but before the buds swell, trim the top tips 1/3 of their length. Trench down along the former dripline about the radius of that circular trench. You will need burlap, canvas, straps and ropes, some levers too and you may need physical help and you'll certainly need a spade.
After some minor carnage of root tissue, and once the root ball is wrapped snug and hoisted up out of it's bed, find a cool spot to store it for transport in the spring. Water and mulch the root ball until then and it always helps to heel-in the ball by scraping a shallow bowl to help keep the roots moist and out of the drying wind and deadly sunlight.
How large a tree can be "bare-rooted" for planting? Read this voluminous essay I just did for a 12" caliper tree. Yours is most definitely a great specimen to transplant but you need to get it acclimated to a concise root ball asap. Dig a trench 1' radius from the trunk. 1' wide. 1' deep. Fill with straw. Do this now and in the early spring before the sap starts running, the buds break, transplant to new spot. Do not leave this tree's root ball out of a hole for more than a few hours.
I also think you should leave where it is. Look @stormy answer, if you want to move it.
The plant is very small. I assume that you can get a similar plant cheap. Look for a nursery nearby you. For trees I doesn't recommend garden shops (often you see that such plants are not so good, they have been in pot for for much and possibly they come from away (so not acclimated for UK)).
I think for less then 50 pounds your should find a similar tree (maybe slight smaller). But hurry. Autumn is the ideal period to plant bare root trees, but you still have some time before full spring come out.
So, @stormy solution is correct, but if you are not in gardening, it will be not so cheap (lack of tools). OTOH the cherry tree on the picture seems too close to the house (if it is a sweet cherry tree), so possibly it should be moved anyway.