If it's a council run site they do the assessment and the results are usually posted on-line (Google search shows many reports) or can be made available for viewing at the Allotment Society's AGM.
So yes, whoever is running the site does the assessment, and plot holders can eventually see the final report. Presumably if something dangerous is found on a plot, they would be advised of the problem and remedial work advised, if the responsibility for the work is the plot-holder's..