If you do not need a reference or your wages/ holiday pay/bonuses paid up to date, just don't go in! You need a P45 though and so it is best to serve notice. Other than that, refer to your company handbook on terms or employment/notice periods, this varies depending on your length of service. If you are on a probationary period it can be instant. (On both sides)
I highly recommend you consult with ACAS on any employment law related questions. Otherwise if you have a Citizens Advice Bureau near to you, go and visit them!
You can browse ACAS's website on - www.acas.org.uk
They have been of great help to me in many an employment law problem! Even when I thought I didn't have any rights, you'd be surprised at what they may tell you!