After the Burning of Parliament in 1834, Cust proposed that the new Houses of Parliament should be to a design chosen in an open competition. He prevailed on Sir Robert Peel, Prime Minister in late 1834, and a competition was held. Cust in this way successfully opposed the appointment of Robert Smirke to be the architect. Peel was replaced by Lord Melbourne as Prime Minister in April 1835, and it was decided to proceed with the competition along Cust's lines, with the style limited to Elizabethan or Gothic, so rejecting the neo-classical.