If you have been working there for over two years, you are a de facto permanent employee, and are entitled to all statutory protections of same. Your employer is ignorant of the fact that there is no onus on you to sign a contract to be protected. In the event of a dispute to the Employment Appeals Tribunal, the EAT will infer a contract of employment that is generally more protective than if you had actually signed a contract that your employer had drawn up.
So yes, you certainly have a case against your employer in this regard