The Charity was established in 1693 by the Will of Edward Storey, a Cambridge captain, gentleman and bookseller. He left instructions that if his son should die without an heir of his own, his estate should be used to buy land in Cambridge and to build ten almshouses upon it. Ten almswomen were to be appointed: four widows of ministers of the Church of England, two widows and one maiden of the Parish of St Giles and three maidens of the Parish of Holy Trinity. All were to be at least forty years of age and of sober life and conversation. The almswomen were to be given £10 per year out of the rent and profits from the estate. They were also to receive annually a gown of sad-coloured cloth to the value of twenty shillings, two pairs of shoes and a pair of stockings at Christmas and mid-summer.

The Foundation now provides 48 sheltered flats at Storey's House, 16 residential care rooms at Edward House, four sheltered flats at Mount Pleasant and eight sheltered bungalows at Vicarage Close, Melbourn, near Royston. It is run in accordance with a comprehensive Scheme prepared by the Charity Commission sealed on 7 October 1999. The Trustees meet regularly to discuss the running of the accommodation and to consider applications for grants.

The Foundation is administered by nine voluntary Trustees, of whom four are appointed by Cambridge University and five are co-opted. The administration of the Charity is carried out by the Clerk to the Trustees and Chief Executive Officer with the help of the Treasurer, the Deputy Clerk and an Administrative Officer. Day to day running of Storey's House and Mount Pleasant is carried out by the Warden and her Deputy. Edward House is run by the Manager and the Deputy Manager along with care, catering and domestic staff. Residents at Melbourn are supported by the Warden of the adjacent South Cambridgeshire District Council properties. A Maintenance Officer is employed to undertake and supervise repairs and maintenance for all locations.