don't know the law but.....
Firstly, are you employed as a self employed person or as a salaried employee?
Secondly - have you actually signed this contract?
Third - is that for "a year after signing" or " a year after leaving"?
Regarding the first point, a full time employee might be reasonably expected to dedicate themselves to the company, or at least not do work for direct named competitors of the company.
A self employed person is basically a business who can do work for a number of clients, if those clients are in competition - tough.
I have seen contracts for self emplyed individuals where it states something like "you will give preference to our reiquirements..." i.e. don't be spending 30 hours a week working for somebody else.
Other contracts state that you can work for other companies in the field, but with prior approval.
I would suggest that if you have signed a commercial contract then your employer is agreeing to take you on the strength of a written promise by you, and could reasonably dismiss you if they found out you were working elsewhere.
I'd advise you to state that you would like to do other work (nixers! even) and that you should be able to prove it won't damage the commercial interests of your company or benefit a direct competitor. I have seen such arrangements work in the past.