Photinia Red Robin. Because the weather is so wet and warmish ( and certainly not hot) and the soil so wet you are probably OK moving it now if you need to. Yes I would give it a trim and move it with as big a root ball as you can manage.

Autumn is normally recommended for moving plants but I think this year you could take a chance and move it anytime.

There is always a chance that the plant wont like being moved and you may lose it.....but there is only one way to find out !!

If you like where the plant is currently, but its just that its got too big, you could try renovating it. You'd need to do this in spring, around end of May time, when you can cut back to make a low framework, removing 2 thirds of the top, then shaping and removing new shoots if necessary as they grow. Thereafter, prune in May or by mid June annually, taking slightly more than you'd like - they grow a good foot in a season anyway, if not more.

The red leaves are new leaves which will eventually go green. These shrubs can grow tall and more tree like, so if you wish to keep it under control and red leaved you will need to keep it cut back. It can be used as a hedge.