Well, it will prove that you're a "bona fide" tenant, which is one of the requirements for qualifying for Rent Supplement - I'm not saying you weren't a bona fide tenant, but you had no documentation to prove it which is what the HSE are looking for.
The relationship between you has to be professional (landlord/tenant), rather than as brothers. Get the lease agreement and go back to the CWO explaining that you didn't know you needed one. If the decision is still the same, then appeal.