Climbing Food?

I was going to say a small one person size pumpkin like a Hooligan...

but then you said fruit

I can only think of getting a self-fertile Kiwi 

Forget the fruit.

Alderman peas! mmmmmmm.

Hope not, mine have only been in a few days.

You can buy apples and pears and train them as cordons - it involves a little pruning - I saw this done by Geoff Hamilton on quite a scale and the show was recently repeated on Blighty - I think it was his organic kitchen garden series - unless of course you want the crops for this year in which case sorry ps Focus are selling fruit trees which can be used as cordons

tayberries climb

With time and patience you could train most dwarf fruit trees over it, I'd have thought, but it would take time. Outdoor cucumbers are pretty good at climbing too, albeit short lived. You could do a combination, have something pretty (like sweet peas) scrambling up quickly over a more permanent backbone of something slower growing, like trained fruit trees.

I did once have a beautiful passiflora in my garden that had started out climbing up a fence, then went berserk and ended up climbing about 25 or 30 feet up into old oak and ash trees that were alongside the fence. In flower it was stunning and it did have fruit every year. Sadly, one year it just simply gave up and died, no idea why, but it must have been pretty old.