My understanding is that you would have to resign first before you can claim constructuve dismissal. You would then have to argue that the company put you in a such a position as to make quitting the only option. There is more info on this link, which suggests that at the very minimum, you need to raise the issue with a manager (this gives them the chance to redress what you may eventually quit over). Do you have a grievance policy? Most companies do and lodging a grievance will certainly help if you later decide to pursue the constructive dismissal path - especially if you lodge a grievance and they fail to follow their own policy.
http://tinyurl.com/nwoz4o
Hopefully you'll get some more concrete answers. In the meantime I've always found ACAS to be very helpful. Good luck, sounds like a horrible situation.