Sorry to dig up an old thread, but this does remind me very much of some of my own antics.
20 something years ago when i was at St Peter and Paul's primary school, i found 2 bullets in the gravel shingle surrounding a path. I was always interested in the war, although a pity i didn't know about the Spring Lane AA gun site as i used to live on Fern Road almost opposite, and did play on the site.
I suppose due to this, i could recognise a bullet at somewhere between 7-9 years old (me, not the bullet

)
At the time, our general council of classmates decided it was from a Spitfire testing it's guns. Obviously now, i know that isn't the general procedure, but with no other reasons for bullets to be on a primary school, a plane is quite likely.
I did try to keep hold of them, but the last time i tried to locate them, they were long gone from the draws of junk a child collects. What i do remember is they were the classic pointed rifle style, some rifling marks on them, but not deformed from hitting anything.
They were most likely .303, or within that range, but in all honesty, without getting a micrometer on them it can't be sure.
Whilst it'd be nice to think they were fired from a defending Spitfire in '41, there is every chance they could have been German.