Open Question: If I leave work on medical grounds can I receive Job Seekers Allowance?

I am having alot of problems in work with management and my colleagues who are related to them. I have been signed off on stress leave and my doctor said that she can not see me returning to work for quite a while with whats going on. I have self harmed and ended up in hospital when I came to write a grievance and so my doctor has told me to leave it for a few weeks and then pick it back up again. I think doing a grievance is very stressful to me, and more stressful because I know that nothing will change if I return to work. Things will only get worse. I know this because another member of staff has put in a grievance about similar issues and they still continue to get bullied by colleagues and management. I have an appointment again with my doctor next Friday and she has already told me that she has no doubt in signing me off sick again. I'm not enjoying being out of work at the moment and am desperate to find a new job and cut my loses with my current place of work, and not have the hassel of a grievance. I am aware that it is illegal to look for work and go on interviews whilst on sick leave and obviously can not pay rent and bills if I just quit my job. I have looked at information on the internet regarding Job Seekers Allowance and have seen that I am not entitled to it if I just quit my job. So I was wondering, if I speak to my doctor, would she be able to sign me off work completely due to medical grounds and advise that I look for other work. If so, I can then claim job seekers and actively look for another job which is the only solution I can think of. Im a bit hazey regarding benefits as Ive not claimed benefits before and have always worked since I left school (I am now 22 years old).