Glasshouse Yard was historically a parish liberty and extra-parochial area (outside the control of any parish). It was made a civil parish in 1866. In 1889 it was transferred from Middlesex to the newly-created County of London and in 1900 became part of Finsbury Metropolitan Borough. Finsbury Metropolitan Borough was abolished in 1965, becoming part of the London Borough of Islington.
For more information, see the EN Wikipedia article Glasshouse Yard. This article explains the former history of Glasshouse Yard.