Alexander Halley was born at Dunkeld in Scotland in or about 1824 and educated at Edinburgh University.
In 1849 he married Emily Jane Harland. The marriage was registered in the district of Scarborough in the North Riding of Yorkshire.
Doctor Halley appears on the 1861 census, living with his wife, six children, and four servants at 7 Harley Street, London. In 1871 the family were living at 16 Harley Street.
Dr Halley was Honorary President of the Gaelic Society of London, and a life member of the Gaelic Society of Inverness.
He died in London on 25 February 1875, aged 51. The following report of his death is from the Morning Post (27 February 1875): 'ALEXANDER HALLEY, M.D. - The death of this gentleman is announced as having occurred from paralysis at his house in Harley-street, on Thursday, somewhat suddenly. Dr Halley was seized with a fatal illness on the morning of that day, and, notwithstanding the anxious efforts which the medical skill of his friends Sir George Burrows and Dr Garrod could exert, it terminated before the evening of the same day. His death may be considered premature, as he had not reached 60 years of age. He has been in general practice and as [sic] physician in London for 30 years, and was well known and highly esteemed by his professional brethren, and among all with whom he was associated in social circles. Dr Halley attended a general court of the Highland Society on Saturday, at which he advocated with earnest zeal a contribution towards the institution of a chair for the Celtic languages in the University of Edinburgh. He leaves a widow and family of seven to mourn his loss.'
Photographed by Camille Silvy of London on 23 June 1861.