Wyatt was elected to the Royal Academy in 1785, and took an active part in the politics of the Academy. In 1803 he was one of the members of the Council which attempted to assert its independence of the General Assembly of Academicians, and when the resultant dissensions led Benjamin West to resign the Presidency in the following year, it was Wyatt who was elected to take his place. But his election was never formally approved by the King, and in the following year he appears to have acquiesced in West's resumption of office. Wyatt was one of the founders of the Architects' Club in 1791, and sometimes presided at its meetings at the Thatched House Tavern.