Don't know if this is of any help, but I was at Heathrow for pre employment medical the other day and brought this subject up. I was told that the problem is with regard to the dimensions of the workstations being designed to accomodate people within a particular height band - not sure what the relevant heights are I'm afraid. Apparently people taller OR shorter than the design parameters are likely to suffer problems (back or eyesight I would imagine) in the long term.
Similar restrictions apply to civil and military pilots which vary depending on aircraft type.
I realise you must be very disappointed about the withdrawal of your job offer but I doubt whether legal action is going to get you very far if NATS are able to assert the probabilty of long term health problems if they were to employ you.