Possibly not the best advice you can have.
I was a full time union rep a few years ago and would suggest you speak to the chefs superior. See if you can get colleagues to support you.
As far as going off sick with stress is concerned, and then waiting to be sacked and going for constructive dismissal, it may never happen.
If they dismiss you it is not constructive dismissal as it is a straight dismissal. It is constructive if you leave because of somthing that has happened to prevent the working relationship continuing. Even then you would need to prove two things
a) it is constructive dismissal
b) the dismissal is unfair
If you go sick, and are sacked, it may be a fair dismissal under 'frustration of contract'. ie you are not fulfilling your side of the contract as you are not reporting for work.
Sounds totally unfair, I know, but the law tends to side with employers rather than employees.
If you are in a union speak to your rep, if not, think about joining one. I would suggest Unite, if your employer doesn't currently recognise a union. If there is already a union in the workplace join that one. All advice they give is free (as long as yiou pay your subs) and they should normally be able to sort things out before even thinking about going to a tribunal.
Also, have a look at the company grievance procedure which they must have in place by law.
Good luck whatever your decision.