Baker, was born in Thirsk and in 1864 qualified as a doctor at Edinburgh.1 After a spell in private practice, he moved to York to run a private asylum and, in 1874, he succeeded John Kitching to become the fourth Superintendent of The Retreat, the asylum founded by the Society of Friends and known locally as the Friends' Retreat. He formally retired in 1892, though he remained visiting medical officer to The Retreat until his death in 1910.

During Baker's tenure The Retreat continued its gradual move away from its founder William Tuke's Moral treatment towards medication, diet and hydrotherapy. The Turkish baths and hydropathic treatment suite, suggested by Kitching in his valedictory memorandum, was designed by Baker together with the Retreat architect, Edward Taylor, though hydropathic treatment seems, in practice, to have been limited to the successful use of the Turkish bath.

In 1892, Baker became President of the Medico-Psychological Association (later renamed the Royal College of Psychiatrists) and the association held that year's annual meeting at The Retreat.