What to grow up my fence

I think you have lots of options here, and there's a good stretch of fence to play with, so you could have more than one thing growing there. If it were me, i would be thinking of permanent residents, and the following would spring to mind: raspberries, grapes and/or espalier-trained apples & pears.

But I wonder if perhaps you might be best looking through your wishlist of things you'd really love to grow, and then working out which one(s) will be happiest along the fence. A lovely problem to have!

Annuals like peas and beans seem a good choice to me. I would be nervous buying expensive trained fruit trees on a rented plot that might get scrumped by kids(speaking from experience of having been one of those horrors that went scrumping).

Best to grow what you like, but perhaps with an eye on the amount of work you wish to do - gooseberries for example more or less look after themselves, but a fan trained plum will take a lot of training and care, particularly when young.

Hello TTT and welcome to the Vine.
I'd plant lots of fruit against the fence - raspberries, loganberries, blackberries, tayberries etc - all the cane berries. They'd love being trained against the fence and some would be happy in the shade.
In summer, you could grow beans and peas, climbing squashes, courgettes and cucumbers.
They could be kept quite "narrow" against the fence and needn't encroach on the path.

Thanks for these suggestions. I imagine I will try a few different things as 30m of anything will be too much!

What variety of pea would grow to around 4'? I have had little luck with peas before now.

I wouldn't be too worried about losing some fruit. If that's what it takes for kids to eat fruit then so be it! How easy would it be to limit espaliers to 4'? Can I encourage a larger rootstock to spread over a long stretch of the fence or would i need to put dwarf trees in every couple of metres?

I had discounted raspberries because I didn't want anything thorny growing along the path. Also, I have a spot that gets a bit of shade from a tree in the adjacent garden and I had that earmarked for raspberries. Is this right?

Raspberries aren't really thorny, they're bristly but not vicious - like blackberries - although there are thornless varieties of those too. They don't mind a bit of shade but need some sunlight during the day.

How realistic is it to grow dessert grapes on an allotment in East Anglia? I have searched the forum a little but it seems grapes are a frequent source of trouble?

You can grow espalier any height you want but those grown specifically for that tend to be grafted onto a dwarf rootstock to give some control. You can even buy and train step over fruit which are exactly what they sount like, a short trunk say 15" high and a single 'T' limb across the top.
Fruit can take a couple of years to mature so the likes of raspberries, goosberries etc will give a faster return.
I would also advise a good spread of crops of things you like to eat so tomato, cucumber, french & runner beans, peas etc. Add a couple of sunflowers for decoration. On your clay I would also be thinking of firstly digging in as much organic material as possible and then regularly mulch with more as you go to break up the clay. Clay contains lots of trace elements that plants love and compost/mulch will add the other key feel elements to the soil (it's actually the bacteria, worms, beetles, woodlice and micro organisms that provide the plans benefits but they need the organic plant life to feed on).
If you plant 'spaced out' you can often fit a lettuce, Kale or cabbage in between to develope after the peas/beans/whatever are finished so you eat produce year round.
43 Metres is fifteen 10 ft rows! I think you should be alright in there.

Im growing Tayberries along the back and side fence of my fruit and veg garden. It’s planted in the corner and has about 2ft square of ground space to itself.

I haven’t yet decided how I’m going to train it. The simplest option is to train one year’s growth along one fence and the next year’s along the other so it will alternate which fence has the fruiting canes, but I suspect as one fence is South-ish facing and the other East-ish it might be better to move the new canes over to the South fence each year after pruning that year’s fruiting canes.

If you’re just using a single fence with good sun then you could fan them with new canes on one side and old canes on the other. Or you could bundle new canes along the top or bottom in both directions and fruiting canes above/below them. Lots of options.