Although born in Liverpool, Alex moved to London with his family as a child. In 1851 the family was living in Lambeth; by 1861 they were in Clapham; and in 1871 they were back in Lambeth. Alex is recorded in the census of that year as living with his parents and siblings at 5 Cowley Place. He was 29 years old and working as a stained glass artist, a profession in which he became highly regarded.
In 1878 it is known that Alex was working from 64 Portland Road, Notting Hill, and between 1880 and 1894 he worked at his home at 6 Euston Square, St. Pancras. His first wife, Agnes Buckley, moved to 6 Euston Square after their marriage in 1881.
Alex worked for a time for the firm of Cox, Sons & Buckley, an ecclesiastical furnishings company based in London. Note that there appears to no family connection whatsoever between Irish-born Michael Joseph Cunningham Buckley (1848/49-1905), the Buckley partner in Cox, Sons & Buckley, and Alex's wife, Agnes. However, just in case they were related, here is some further information on Michael, taken mainly from the Dictionary of Irish Architects, 1720-1940:
Michael was an antiquarian and designer of church furnishings, of London, Youghal in Co. Cork and Bruges in Belgium, and was active from the 1860s until his death in 1905. He was a son of John George Buckley of Carrick-on-Suir, Co. Tipperary, although the New Zealand Tablet edition of 28 September 1905 tells us that Michael came from an old Youghal family. John, Michael's father, had attempted to emigrate to Newfoundland in 1815 but was captured en route by a French privateer and taken as a prisoner to France where he remained for some time after his release. Michael himself was born in Cahir, Co. Tipperary in 1847 or 1848 and educated at Mount Melleray Abbey School, Co. Waterford, and in Louvain, Belgium. He subsequently served his time as an architect under Brangman of Brussels and in 1881 became a partner in the firm of Cox, Sons & Buckley, ecclesiastical art manufacturers of London. However the firm failed, possibly about 1893 (as the company was taken over by Curtis, Ward & Hughes in that year), causing Michael severe financial loss. He moved back to Ireland, where he established a stained glass and metal works in Youghal, Co. Cork. He also acted as agent and designer for the Decorative Arts Guild of Bruges and was about to bring a number of Belgian art workers to work in Youghal at the time of his death. He died after a short illness on 2 August 1905 at his home, 'Montmorenci', Gillets Hill, Youghal and was buried in the North Abbey churchyard in Youghal. He was unmarried.
Interestingly Alex's brother Clement, also a stained glass artist, was living in Youghal at the end of the 19th century. As the Bookers had no known Youghal connection it many have been that Clement moved to Youghal because he was offered employment at Michael's stained glass works in the town.
Getting back to Alex, his commissions includes glasswork in All Saints Church, Salhouse, Norfolk (1874 - 1899); St. Thomas's Church, Ryde, Isle of Wight (1883); Stoke St. Gregory Church, Somerset (1886); St. Edmund's Church, Costessey, Norfolk (1889); St. Michael and All Angels Church, Booton, Norfolk (1891); St. Mary's Church, Mold, Flintshire, Wales (1891); St. Michael and All Angels Church, Appleby, Leicestershire (1893); St. Edmund's Church, Fritton, Norfolk (1900); and St. Patrick' Cathedral, Auckland, New Zealand (1906 and 1907).
In the early 1990s Alex moved to Bruges, Belgium, where some of the above works were executed. Perhaps he worked with or for Michael Cunningham above who had a branch of his business in the city. We know that Alex was resident in Belgium in 1894 as an article in the Cheshire Observer of 14 April of that year on the installation of his stained glass window in Mold Parish Church refers to him as having moved to Belgium from St. Pancras. It appears that he had moved to Brussels from Bruges by about 1907 as mention is made of the stained glass window by 'the well-known artist Alex Booker of Brussels' (according to the New Zealand Tablet edition of 14 February 1907).
Sometime after returning to London Alex and his second wife, Theresa (a sister of his first wife, Agnes) lived in St. Scholastica's Retreat, Kennington Road, Clapton. The Retreat, now demolished, was designed by architect E. W. Pugin and was built to provide accommodation, in self-contained units, for elderly Catholics of diminished means.