I find them in every gardening store in spring and just before winter. But I'm from the mainland, you can try if
@Clorgan might've seen a few somewhere. She seems to have her ways of turning things into a positive upward spiral for everyone and I remember recommending her to get some beeches.
I tried googling 'fagus sylvatica UK nursery' and I found this page:
Buy beautiful Beech Trees (FAGUS SYLVATICA) .Retains golden leaves in winter.High quality trees, hedging from Tree Shop. Fast UK Delivery.
www.tree-shop.co.uk
At 2.2 quid a piece I think they're pretty expensive but they are the same size range as we get them over here. You should be able to find better results if you put in a bit more effort than I did (I just clicked the first link).
Here's a cheaper one, they seem to go per bundle of 25. But you'd have to wait until october.
The Common Beech is very popular as a standalone specimen and make great alternatives to fences or walls when grown as hedges. They are majestic looking, with thick branches and smooth grey bark. It’s has large glossy green leaves and small flowers, as well as producing nuts that ripen in the...
www.hedgenursery.co.uk
I think
@Peter44 has some experience with bare rooted beeches. I remember he wasn't really happy about them, he might be able to chime in with some advice about what to take into consideration.