Alexander Burnett was the second son of Catherine Ramsay, the granddaughter of Sir Charles Ramsay, 3rd Baronet of Balmain of the earlier creation (1625) in the Baronetage of Nova Scotia, which was inherited by her brother, Sir Alexander Ramsay-Irvine, 6th Baronet.

Sir Alexander Ramsay, 6th Baronet bequeathed his estates to his nephew and the baronetcy was revived in favour of Burnett a few months after Sir Alexander's death, who changed his surname to Ramsay by royal licence.

The seventh and present Baronet is the presumed heir to the dormant Burnett Baronetcy of Leys.

His son Sir Bertram Ramsay was an admiral in the Royal Navy.

[1] The heir apparent to the baronetcy is Alexander David Ramsay of Balmain (born 1966), eldest of three sons of the 7th Baronet.