Sited just to the east of Charing Cross, the picture source, Wikipedia, has a very useful map, but there we also read that the garden "did not reach all the way down to the river" which rather contradicts London Gardens online which says the Kent arch "was originally a riverside entrance of Northumberland House".
The House was built by Henry Howard, 1st Earl of Northampton, from whom it passed to another branch of the Howard family, the Earls of Suffolk who were also the Dukes of Norfolk (e.g. Thomas Howard, 4th Duke of Norfolk and Admiral Thomas Howard, 1st Earl of Suffolk). In the 1640’s the Earl of Northumberland acquired it cheap as part of the deal when he married a Howard. It remained the London residence of the Percy family, the Earls and Dukes of Northumberland, until Victorian times, when many houses of this age were lost. Following a fire the Duke sold and the house was demolished to make way for Northumberland Avenue.
Known as Suffolk House when owned by the Earls of Suffolk. And just to confuse things further: do not confuse this Charing Cross Northumberland House with the Northumberland House at St Martin le Grand.
The lion over the arch,that you can see in the image, was relocated to a gateway at Syon House.