A contract doesn't require a witness for it to be valid. It doesn't require a signature. It doesn't even require a written document. (Every time you buy something in a shop you've entered into a contract with the vendor).
Having a witness to a signature might be regarded as a wise precaution in certain circumstances but the absence of a witness in no way invalidates the contract. (People like Richard Branson will sign contracts involving millions, or possibly billions, of pounds. I doubt that Mr Branson has ever had anyone witness his signature except when writing his will. It's simply not required for a normal contract).
Chris