Your employers have a duty of care towards you and are responsible for the actions of their employees; presumably this harassment is not on the grounds of sex, race, disability, sexual orientation or religious belief. As f 30 says you have difficulty with a remedy if you have only been with your employer for 10 months (1 years service is required to go to an employment tribunal), your best advice is probably to remain with your current employers and follow your grievance procedure putting your case without becoming emotional, I know this is not easy. If you are a member of a trade union contact them, they or another employee can accompany you.
There are five potentially fair reasons for dismissal:
Capability
Conduct
Redundancy
Contravention of a statute
Some other substantial reason.
Do not try constructive dismissal as Eddie says you may then have a problem claiming JSA as you have made yourself unemployed, it is also very difficult to prove constructive dismissal and remember you do not have a remedy until you have been with this employer for one year.
Probably not the advice you wish to hear but stay and go through the grievance procedure.