On 8 February 1708 he was consecrated Bishop of Chester: this was at the personal wish of Queen Anne, who overruled the advice of her ministers in appointing him. He was Archbishop of York from 1714 until his death in 1724 and a Privy Counsellor. He owed his advancement to the good will of the Queen and of his predecessor, John Sharp, who had a great regard for him, and had great influence with the Queen: it was Sharp's dying request that Dawes succeed him at York, which the Queen happily granted. He restored the Archbishop's palace in York, the Bishopthorpe.