Damp cool - I'm torn between saying move them now, because the weather's cool and damp, which is good for moving plants, or saying wait till they've flowered, by which time it might not be cool and damp, it might very well be hot and sunny and dry. You may well lose the flowers if you do it now, but from a long term point of view, I'd be inclined to do it now anyway and make the sacrifice.

Many thanks :) I am a novice so any advice from someone with experience is greatly appreciated.

Agree if you have to move them before autumn do so now not in mid summer and keep well watered.

Follow MG's advice on the watering - didn't realise you were a novice. Try to get a good sized rootball and try not to break roots when you dig it out. Hopefully your plants have not been in the ground longer than 3 years, otherwise its a mammoth task. Dig out with a fork, not a spade, so you don't inadvertently chop through roots. YOu may need to excavate some soil with a spade once you can see what you're doing, but otherwise, its a hands and knees job, carefully teasing out the longer roots.
When replanting them, dig a hole that's both wide and deep enough to accommodate all the roots you can see, without cramping them up or bending them to fit into the hole. Add humus rich material such as composted animal manure or soil conditioning compost to the area before replanting, and dig the whole area before making the holes. Keep well watered - at least a gallon a week, maybe more for the first few weeks. And, plant somewhere shadyish and damp if you can.

And water even if it is raining, I am making the assumption that you have acidic to neutral soil as the rhodos are already doing well - if not you need to make an even bigger planting hole and add ericaceous compost to.