is it possible to dig up my plants and re-plant them at my new house?

Setting aside how to do it, you need to make sure you have the agreement of the person buying your house. Garden plants are like light bulbs, you aren't expected to take them away!

and its not the best time even if you can

HI Michelle, Just to let you know, my understanding is that the law actually requires that you inform the property purchasers of what your intentions are and come to agreement with them. This is a legal obligation. Better safe than sorry as well. You don't want to risk a dispute developing afterwards. With kindest regards, JONATHAN H.

Readejahn is right, I don't know about English law as there are a lot of differences but here in Scotland the new purchasers could make a claim against you if you dug up and removed plants after the sale is completed. If plants are in pots they don't become part of the property in the same way, although there are still exceptions in these cases too.

Quite often though you can come to an arrangement with the new purchasers.

If you are going to move the plants or bushes, it is only really worth it if you can dig out practically all the root and put it in a decent sized pot with compost and water it well ( but not so that it is waterlogged, the roots will need to breathe). Some plants will still die in these circumstances as it can be too much of a shock but many will pull though and be fine.

be better if you can work something out with the new buyer if you can move them in autum to when there dorement excuse my spelling lol

Jonathanhales is exactly right.You must tell your buyer what you are atking abd not including in your sale. Unless they are very special plants I wouldn't bother to move them. When I moved in June some years ago ,I planned beforehand and potted up specials, except for a lovely tree peony which I cut back hard end of May after flowering and put it in a large pot, it has done really well ever since, see my 'photo of it!!!

hello and it woulkd be better when there dorement

you could always take cuttings?

saves any type of argument then

x x x

Unless English law is different than Scottish law on this point you would need to have stated in the sales literature that specific shrubs/plants were being removed, actually named them and marked them in some way so that any potential buyer would know they were not getting those. So that is the first issue you need to address.
Setting that aside this is not a good time to move any plant/shrub it will set the plant back as it is in full 'growing mode' right now and can't pull its energy back down into the roots. As Noseypotter says if you can get agreement with the new owners you need to wait to autumn to move but, frankly, unless you have a very valuable plant/shrub why not leave them where they are and start again?

Think of the fun you'll have with your new garden!