From the Wikipedia page [1]
Northumberland House (also known as Suffolk House when owned by the Earls of Suffolk) was a large Jacobean townhouse in London, which was so called because for most of its history it was the London residence of the Percy family, who were the Earls and later Dukes of Northumberland, and one of England's richest and most prominent aristocratic dynasties for many centuries. It stood at the far western end of the Strand from around 1605 until demolished in 1874. In its later years it overlooked Trafalgar Square.
It was demolished in 1866 after a fire and Northumberland Avenue constructed in its place.
For the student accommodation see [2].