Firstly I would contact the secretary of the site if they have one,if not contact the allotment owner IE local council,or whoever,explain that your uncle has been doing most of the work over the last few years and has benefitted personally from it and for health reasons would like to take over the plot,they might well say that he cant have the plot he has been doing,but if there is no waiting list possibly offer him one of his own,i hope this helps,good luck,let us know how you get on.I'm sure the plotholders on site will give you the advice that you need so talk to them too,to see if there is a procedure that you need to follow,most plot holders are very helpful.