FWIW, I grew up in or near: Uxbridge (2 years), Crawley Down (4 years), Bramhall (2 years), Loughborough (10 years), and during that time went to 4 different primary schools and one secondary school.
1. The space between two buildings containing a footpath: 'jitty', 'cut-through', 'alleyway'
2. A knitted item of clothing worn over a shirt, without buttons: 'jumper'.
3. The act of not going to something that you're supposed to go to: 'skiving'.
4. Playground game in which someone is "it" and has to touch someone else who then becomes "it.": 'tig' (and variants became 'tiggy-' e.g. 'tiggy-off-ground')
5. Playground truce term when you want a break from the above games: 'barley', I think, but not sure if that's genuine memory or interpolation from having read Opie & Opie. Nobody took any notice of that sort of wussy nonsense anyway.
6. Playground term you say when you want to claim something: 'bagsy', but with claiming a desk in the classroom it was always 'SAVED!' (shouted while loudly slamming books, pencil-cases, etc down on the desk in question)
7. Slip-on shoes worn for school sports in the days before trainers: 'pumps', later 'plimsolls'
8. Small round bread: 'roll' or 'bap'.
9. Sweet course that follows the main course: 'pud'. NB we were always outraged if my parents said that there was pud & then it was only fruit. "That's not pud!" Not that fruit is a bad thing, but it's not pud, is it. (Depends on the fruit, though. Apples == not pud. Strawberries == pud, obviously. Clementines are sort of nearly pud, but still more fruit than pud, really.)
10. Scone: pronounced to rhyme with "gone" or with "moan": to rhyme with 'gone'.
11. Generic term for a bird: Er. 'Bird'?
12. Round food stuff made with batter on a griddle, which is brown on the outside: 'pancake'? The griddle is confusing me here, it sounds more like drop-scones, but that seems a bit obscure.
13. A delicacy that you feel is particularly local to you: can't think of anything...
14. Term of endearment: 'honey', 'sweetie'... all sorts of things, nothing particularly localised.
15. Someone who's soft and easily feels the cold: 'wimp', probably.
16. Tourists: we didn't have those in the Midlands. :-}
17. A field boundary: 'hedge'.
18. You see a group of animals standing in a farm building. They have udders and go moo. Complete the following sentence: "Look at those ____ standing in that ____!" : 'cows', 'barn'.
19. You haven't had anything to eat in a long time, and your stomach is letting you know about it. You would also like to be warmer. You say: 'I'm cold and hungry!' (or 'freezing and starving' depending on how whiney I'm feeling)
20. Your friends invite you to enter a haunted house: you demur. What do they call you, by way of a derisive taunt?: 'scaredy-cat'.
21. A man who dresses flashily with lots of expensive jewellery is a ____: er, dunno what they're getting at here, sorry.
22. What do you say in a shop when you are handed your change?: 'thanks'
23. Generic friendly greeting: 'hiya', 'hi'
24. Slang term for a pair of trousers: can't think of one...
25. Slang term for left-handed: can't think of anything specific, but left-handed kids would've got called 'spaz' more than others, probably.
26. Pronunciation of Shrewsbury? Newcastle? Glasgow?: sh-ROSE-bree, new-CASS-ul, gl-AZ-go.
27. Two pieces of bread with a filling: 'sandwich'.
28. A playground way of saying someone is out of order: not sure... though like taimatsu I thought of the way of saying "UmmmmmMMMmm!" or "AmmmmMMMmmm!" (usually followed by "I'm telling on you").
29. Dialect terms for hands, ears, face – and, indeed, for any other body parts you care to name: can't think of any.
30. Terms for someone who looks miserable: can't think of any. (These days my brain says CHEER UP EMO KID. New dialect!)
31. Potatoes: 'spuds'. I would just like to add that my dad calls parsnips 'snibs', or 'snibboes', which always makes me smile.
32. Pale round food stuff with a brown base, lots of holes in it, which you serve hot with butter: OM NOM NOM. Oh, no, hang on, er, 'crumpet'.