If you are working illegally in a school, and you would be as you are breaching statutory requirements, then technically you are not insured. The employers insurance company would not cover you or the school. You, the school, and the agency are therefore personally liable and if a claim is made for damage then it will be up to the courts to assess responsibility and costs. The school Governing Body can also be charged as failing to enforce a standard employment check therefore breaching both Health & Safety and Financial regulations that all staff must be appropriately covered.The agency can also be sued for failing in their contractual duties. You need to task the agency to provide you with long term cover of a term or longer to ensure that induction can be served.