If there are one or two plants with a sentimental value, then I would ask if I could delay moving them until the spring. Sometimes it is better when you move and have a new garden to make a completely new start with a new design and new plants.

Have you told them that you will be taking plants in the sale? if not you have to leave them by law. why not ask them what they expect you to leave or what you are able to take?
that way you will have a clear idea on what can and cant be taken.
when we moved here 20 years ago I was really upset to see what they had taken as the purchase was to include those plants in the ground. it looked like a bomb site, just holes and damaged trampled plants either side. Pots etc are fair enough.

The plants if lifted with a good root ball and put into pots will survive as long as you keep them well watered. It is a good time to take divisions of many plants. I'd cut the foliage down by half to reduce water loss in any winds we are bound to get. they will stay in the pots happily until you know where they are going in your new property.

What a pretty house Youngalastair. Is it the old or new one?

It's a difficult decision when moving house just what plants you can't bear to leave behind. What have you got to lose? Why not take a small rooted section of your most favorites and put them in pots? You may well be surprised at how many will still grow for you.
You could also try taking stem or root cuttings but they will probably need much more nurturing than the already rooted plants.

Can be an emotional affair, we have moved several times and have now compromised with myself, I take no more than five plants that have special meaning for me and never go back afterwards as whatever the new owner does is rarely if ever comforting.

We've moved several times too and I did go back to one house over 20 years later. When we bought it the previous owner had grafted all his own rose bushes and, mixed with tall and healthy delphiniums, the front garden was a picture. People used to stop and exclaim. I only ever considered myself a caretaker for that garden.

So when we went back, just because we happened to be in the area, I was appalled to find that a subsequent owner had cleared the lot for an extra parking space and a tiny lawn. What a waste.

We moved last year and the person who bought the house hasn't a clue about gardens. He's going to rent the house out and has used weed killer rather than hand weeding
so has killed lots of plants. I still visit my old next door neighbour so it's hard to miss. I just couldn't take everything, just a few favourites. I made that garden from scratch, every shrub, plant and blade of grass and it took years. Never mind look forward and not back, that's my motto. Good luck with your move.