You do have a contract - you work doing a specified job in return for money.
Both you and your employer can be in breach of contract and you have the same employment rights as anyone else.
What you don't have is a written statement of employment particulars. I would always prefer to have at least the basics in writing - you should be supplied with one within 2 months of starting employment.
Ask your employer for one. If he doesn't provide it, write it yourself and ask him to sign it.
http://www.businesslink.gov.uk/bdotg/action/st mtEmpLanding?r.l2=1074428798&r.l1=1073858787&r .s=sm&topicId=1075225309