Plants for a yield, but also a tidy(ish) hedge? Strategy for planting?

After 3x years of battling rabbits and pigeons, and finding new plantings eaten to the ground in 12 hours on many occasions, I am succumbing to fencing in our veggie garden. I will be fenced with rabbit-proof fencing to the ground, most likely with rocks all around the base to discourage any digging (burying fencing where we are, tends to end up with a rotted wire after 2/3 years). I resisted for a long time as I do not want a big ugly fence in my garden, but I live on the edge of woodland, there are burrows in my garden; I cannot have veggies growing without protection.

Seeing this as an opportunity, I think a hedge in the European 'potager' style would be fantastic and the new 'edge' provides an opportunity for a yield, so I want to plant a hedge to swallow the fence; best of both worlds.

I wanted to see what experience others have had with plants that would suit such an application; 1m or so high (I really do not want to be pruning too much), and offering a yield. Not climbers so much (although they may be helpful), but something thick that is good for losing/hiding a fence. What plants might suit such a brief in zone 8/9 UK climate? All four sides get four different aspects (of course), full sun, morning shade, afternoon shade, and relatively high shade, so there is plenty of scope for diversity. I have considered blueberry and hazel (although that would have to be managed and pruned a lot - like a traditional non-permie hedge) and have currants, honeyberry and Japanese wineberry nearby.

Any experience anyone has of planting around a fence would also be great to hear; did you grow alternate plants on either side of the fence or just on the side, you wanted to hide? What was your strategy?

Many thanks.

I do not want a big ugly fence in my garden

Could you live with a wire mesh fence built with posts and pulled straight?
Or this sort
And then groiw the stuff to hide it.

My fence is definitely not rabbit proof but one section is if I wanted it to go all the way around... We framed cattle panels with strips of cedar and installed them between cedar posts. We wanted the top to be even and not sit straight in the ground so the gap at the bottom varies 1"-4", plenty of room for a bunny. But along one section, we built a narrow 12" wide raised bed. We used 8" wide cedar boards so it overlaps the bottom gap of the fence. And in that narrow space we planted raspberries. It is doing extremely well. During the summer it is a thick wall of green and we easily pick raspberries from both sides of the fence.

I went outside and took some pictures of my raspberries and the fence. You would want to have fencing with smaller holes for year round control but the raspberries are so thick from April to October that the rabbits would have a difficult time getting through.

I also have roses growing on one section of fence. I was hoping for some nice rose hips but these roses are not making any even though they should.

My dad has a similar style fence with smaller holes. He has blueberry bushes on one side and strawberries on the other side, though they don't cover up the fence at all. Last year he grew beans, peas, squash, sunflowers, and cucumbers all over it.