I think the employer has a duty to ensure that his employees are safe in their work. and that they are not being a danger unto themselves healthwise.The employer should also ensure that the employees understand what this questionnaire is required for,where the given information will be kept, and who will have access to this information.
All this info is available from the employees GP, and with the agreement of the employee could be released to the employer.
Questionnares are frequently not filled in accurately because dates , illnesses accidents of a minor kind are often forgotten, and some things are deliberately left out.
Would you want to put down ,for example, that you are being treated at the moment for say ,some sexual disease, and this info could be read by say the tea lady because it has been left out on an office desk.
I am always personally very uneasy about the confidentiality maintained in a work situation.
What does your Union think of the questionnaire?