Pete wrote ...
For 2 seasons now, an area of the allotment : 2 x 1 metres, refuses to
produce anything - not even weeds. I transplanted some brasica seedlings
in Spring. Outside the dead area, these grew to full size. Within this
area, they withered and died (took about 4 months and they didn't grow
higher than 4 inches).
Prior to my taking the allotment over - it had been overgrown for about 7
or so years. Any ideas would be appreciated.

Does anything grow on that spot Pete? Weeds?
If nothing, then you have some seriously contaminated soil and your Council
should be told about it, they should do some tests and get it changed for
you if it's only a small area.
Maybe it was the site of a shed and the chemicals got into the soil, or
someone used their plot for dumping something.
Recently there was a problem with an allotment site in Chertsey where the
Council wanted to built but found contamination, panic, panic, I understand
it turned out to be a previous gardener that poured his old engine oil onto
one spot of his plot. (but don't quote me on that)

--
Regards
Bob
In Runnymede, 17 miles West of London