Burgh House is a historic house located on New End Square in Hampstead, London, that includes the Hampstead Museum. The house is also listed as Burgh House & Hampstead Museum. Burgh House was constructed in 1704 during the reign of Queen Anne. At the time of construction the Hampstead Wells Spa was flourishing. In 1720 the S…Burgh House is a historic house located on New End Square in Hampstead, London, that includes the Hampstead Museum. The house is also listed as Burgh House & Hampstead Museum. Burgh House was constructed in 1704 during the reign of Queen Anne. At the time of construction the Hampstead Wells Spa was flourishing. In 1720 the Spa's physician, Dr. William Gibbons, moved to Burgh House, which he enlarged. He added the present wrought-iron gate which carries his initials.