The simple answer is yes, if 4 weeks is stipulated then it applies to either party. If either party ignores the notice period then the employment contract has been breached.
Depending on your relationship with your employer you could try to negotiate a shorter period when you resign; however you should not agree to a start date with your new employer without first agreeing this. Generally, most employers will be willing to negotiate (they're not all ogres!) as it's often not in their interest to enforce the notice period unless your role is business critical. Nor is it likely they would pursue you legally if you did decide not to complete the notice period.
You should however bear in mind that if you do leave without working your notice period (and your employer has little recourse to force you to work your notice period) it would be you who has breached the employment contract and this information can be provided in future references: surely not something that you would really want a future employer to see.
And the answer above from anniebird is not correct, see the below link to ACAS which may also help you...
http://www.acas.org.uk/index.aspx?articleid=11 21