You sure could try, but UA paid BA to fly you there. Granted, UA had the original problem, but BA accepted your ticket (and the money from UA) to fly you, so your gripe is with BA for the delay, as it was their service that failed. UA provided you with an acceptable alternative, but BA failed to deliver on their end.
Again, UA is responsible for the delay between the original flight, and the scheduled BA flight, but not beyond that. UA acted as an agent for BA. WHen an agent (brick/mortar, or online) books you on UA, and UA is late, do you complain to the agent, or to the service provider?