You can move it now, may mean it takes a bit longer to start flowering but that is all. Remember to keep watered after moving.

If it's a herbaceous paeony, the best time to move it is immediately after it has gone dormant this autumn. Replant it WITH THE GROWING BUD ABOVE THE SOIL. Also, give it a good feed early next spring

As I remember, it has never died right down, and is tree like with a trunk (I'll post a photo tomorrow) and is about 4ft tall. I have had the other type but gave it away as it wasn't thriving in my garden. I thought the tree paeony was buried deeper than a herbaceous one.

Yes it is. I had (mistakenly) assumed it was a herbaceous paeony as they are more commonly grown. However, they are often grafted on to the rootstock of an herbaceous one, so immediately it goes dormant would still be the best time to move it

I've never heard of tree peonies being grafted onto herbaceous ones Andrew. None of ours are nor are the ones our friends have - we know as we grew them from seed.

MG - at least one of mine is, as it suckers from the root.
I only noticed when the low growth had a completely different flower from the top growth

Very odd we've been staying with the president of the Scottish Rock Garden Club and her husband and neither of them has ever heard of a tree peony being grafted onto a herbaceous one.

The second pic shows a root right at the front which is coming from the tree. I'm pretty sure it wasn't a grafted tree.

MG - to quote Christopher Lloyd in ;The Well-Tempered Garden;, page 374:
"All the hybrid tree paeonies have to be grafted on to pieces of root of the herbaceous types"
Perhaps things have changed since he wrote that?

Andrew - I can only think they must have... Except the RHS states:

To increase the stock rapidly tree peonies, especially named cultivars, are commercially often propagated by grafting on herbaceous peony rootstock such as P. lactiflora in August and September, but this method is not commonly used by home gardeners. Cultivars can be also grafted on seed raised tree peony rootstock.

So there you go...

I'm not sure of all the technical stuff but do know that all Binnys Tree peonies come with the recommendation to plant the graft 3 inches below the surface. Here's what I've copied from their care advice sheet.

Tree Peonies should be planted with graft 3” under soil surface.
Do not allow your soil to become dry in the spring. This may cause your plants to abort their young buds.
Do not grow in soil that becomes waterlogged Peonies will not tolerate this.
Do not plants in too much shade. Some species and red flowered varieties will grow happily in light dappled shade out of the midday sun.
Follow these simple rules an allow a free flow of air around your plants and you will be rewarded with years of trouble free flowers.

Interesting info from all of you. I shall endeavour to plant it quite deeply before the winter sets in. Watch this space!

Good luck!

And it probably isn't grafted Cammomile...

Update: I have moved it and it didn't like it one bit. I fear I may have killed it but will leave it in until I am sure its had it!

Oh I do hope not! In general they don't respond well to moving but fingers crossed it will survive.

Update number 2. It survived (probably because I threatened to pull it up) and yea - it has two flower buds on it. I shall take a photo when it flowers. After all these years!

Wow great!