[zinnia21]

I've just got an allotment, after a four year wait. Sadly, the shed that was on it burnt down last summer, leaving an area of burnt soil covered in charcoal, nails, glass and bits of half burnt chipboard. My question is, could I just pick out the nails, glass and larger bits of wood/chipboard, and dig the smaller bits in, or would that potentially contaminate the soil? I'm not too worried about the wood but wonder if the chipboard might have left the soil contaminated and unsuitable for growing veg. Anyone got any thoughts on this? Picture attached although not that easy to make out the damage.

[Subversive_plot]

It is difficult to be absolutely certain.

Certainly, the smoke emitted from burning chipboard could have put toxins into the air.  Exactly what kind ... that is the uncertain part.  The same goes for uncertainty regarding any plastics or chemicals that may have been in the shed when it burned.

A good practice may be to pull up the weeds in that area and sweep / collect / bag any loose surface debris from the burn area, dispose with other waste going to the landfill.  I would try to do that as much as possible, rather than digging it in.

[Hampshire Hog]

As Subversive says don’t dig it in. My temptation would be to try to skim the surface removing the top inch of soil and debris over the affected area.

[coldandwindy]

I've just got an allotment, after a four year wait. Sadly, the shed that was on it burnt down last summer, leaving an area of burnt soil covered in charcoal, nails, glass and bits of half burnt chipboard. My question is, could I just pick out the nails, glass and larger bits of wood/chipboard, and dig the smaller bits in, or would that potentially contaminate the soil? I'm not too worried about the wood but wonder if the chipboard might have left the soil contaminated and unsuitable for growing veg. Anyone got any thoughts on this? Picture attached although not that easy to make out the damage.

Well done on getting your allotment!
Do you need to grow veg on this precise bit? You are going to need a shed, paths, somewhere to park your bike(!). Can you design things with that in mind? Or many allotments have an area for growing cut flowers. 
I'd certainly pick out all the bits you can. Don't dig the rest in because you'll be surprised how the weather brings more bits to the surface over time for you to pick up.
Part of our croft used to belong to a dirty so and so who used it to dismantle scrap cars. We moved what we could & grew flowers and Mrs Windy's dye plants on the rest. It's amazing how, many years later now, the frost still brings broken glass & little bits of metal to the surface. We also put up a small greenhouse that we still use for seeds and potted plants, rather than having beds composed of the underlying soil. It is very useful.  (We grow our veg on another area that he didn't have access to.)
Hope that helps.
Good luck with your new plot!