My favourite plants for shady areas are hostas, ferns, foxgloves and the wonderful fatsia Japonica. There are many other alternatives.

Welcome to GoY, Myrtus.
I'd like a bit more info - is there some kind of border you are going to plant into in front of the hawthorn? I'm just thinking about planting shrubs there, which is a good idea given the problems with weeds, but they would need to be planted at least 5 or 6 feet away from any tree trunks such as your hawthorn. Is that achievable?

Thanks for your advice, GoringFolly. I hadn't realised foxgloves could be shady, and hadn't even thought of ferns.
Hi Bamboo - there's about a foot between the fence and the tree trunks, then about 3m between the tree trunks and where we want the lawn to start, so quite a bit of space for planting (it was basically a field when we moved in, and we're just getting to this part of the garden). Ideally, I'd like taller things amongst and just in front of the trees, then more border-y plants closer to the lawn, if that makes sense?
But it sounds as if shrubs would need to be away from the base of the trees, which I hadn;t thought of.

welcome to GOY Myrtus. I'm sure you will find lots of help on here..:-)

Welcome to Goy xx have a wee search for shade plants and see what you can find....loads of great info around the site and some useful suggestions above. Look forward to seeing you around, from another relatively new poster :)

welcome to this wonderfull site . how about weed supressing membrane round your trees and back to the fence and maybe rite up to the grass . you can stop the stingers from outside . plant some lovley plants threw the membrane and use something like broken slate as a mulch .

Dig those Bramble roots out 2.5 feet deep or you will never get rid of them - even if it means going round to the other side of the fence !

Thank you for all your advice - I can see I have a lot of work to do! I've had more of a look round the site, too, and there's so much helpful information. It's great.
Thank you all.

If you have bramble roots near the trees,they will be well nigh impossible to dig out because of the tree roots, but there is a way to deal with those without digging out.

I think your idea of shrubs nearest the trees (and weeds) and smaller, perennial stuff at the front is a good one - its much easier to deal with weeds around fairly large woody based plants. Some shrubs to consider for this purpose which tolerate shade well are Elaeagnus varieties, Mahonia, particularly M. aquifolium and its cultivars, along with Aucuba, Sarcococca varieties, Skimmia, Pieris and Camellia, provided the soil isn't alkaline for the last 3. All these would need to be 4/5 feet away from the tree trunks - they'll grow out at the back as well as at the front, towards the trunks behind, filling in the gap between, and they're more likely to have space for their roots that far from the trees. Get the spacing right and you can plant smaller things in front or sort of in between, just not so far back.

Thank you - loads of ideas that sound good. Will some healthy shrubs like that crowd out the brambles eventually ?(if I keep pulling them up in the meantime)

Sadly not - brambles will increase if left alone - those long shoots they throw out will touch the ground and then root.