Autumn or spring will do. You may find it much easier to cut it right back, it's difficult to move large ones without breaking a lot of the stems and it will recover better. You won't get many flowers next year if you do that though
Unless you live in a very cold part of Britain I'd move it any time now, it'll have a head start next year
hi, I'd wait until flowering and growth for the year has ended. Hydrangeas should be mostly bare wood from November/ December, so if you lift it then with as much root ball as possible, water it well in and keep watering every day for a week or so it should be ok