it depends
It depends on what your contract says, it should stipulate the period of notice which must be given (either by you or by them) during the notice period.

According to the government the statutory minimum notice period is 1 week (providing you have worked there for more than one week)

That said, they are highly unlikely to sue you (owing to it costing far more than they would be able to get out of you) over missing 4 weeks (if for example, it is a 4 week notice period) if you really want to get out sharpish.
(b3tamax Mate, you're fat and I'll throw you in the river, Thu 13 Nov 2008, 11:10, Reply)