- He played for the Muppet show, produced at ATV's Borehamwood studios from 1976, and for Sunday Night at the London Palladium and the Morecambe and Wise Show.
- Plucked from Scotland by London bandleader Jack Payne in 1934, McQuater became part of an extraordinary exodus of brilliant Scottish musicians whose impact continues to the present. Within a year he was in the Lew Stone band, where he replaced the celebrated trumpeter Nat Gonella. A year later, he joined Ambrose's star-packed orchestra, then the obvious choice for classy residencies and engagements in London's upmarket restaurants.
- Performing for the troops, Corporal McQuater and his chums sometimes shared the stage with Major Glenn Miller's American Band of the Allied Expeditionary Force.
- McQuater often performed with John McLevy in the 1970s and 1980s.
- In the 1940s, McQuater joined The Squadronaires, and worked with the BBC Showband in 1945.
- By his mid-teens McQuater was playing with Louis Freeman's band at Green's Playhouse in Glasgow, and he later performed on transatlantic liners.
- Following the early death of his father, he helped out by working at a joinery shop from the age of 13 while practising cornet for six hours every night.
- The mayor's son had a Louis Armstrong record, and this gave the young Tommy his introduction to jazz.
- McQuater turned professional in his teens and got a regular position with Louis Freeman's Band, which played at Greens Playhouse in Glasgow.
- He was among the earliest local players to forge a distinctive personal style.
- Given McQuater's evident jazz flair, it was perhaps inevitable that he would be chosen to record in the mid-1930s with the great US alto-saxophonist Benny Carter, then working in London as arranger for Henry Hall's radio orchestra.
- Called up in 1940, McQuater joined Chisholm and many other prominent London musicians in the RAF dance orchestra, later renamed, more snappily, the Squadronaires.
- After a year with the Skyrockets at the London Palladium in 1951, McQuater opted for commercial music, first with Cyril Stapleton's BBC show band and then, for 17 years, with Jack Parnell's ATV orchestra.
- McQuater was most notable for his work in the United Kingdom with Bert Ambrose in the 1930s, and also for some recordings made with George Chisholm and Benny Carter.
- He continued to take a lively interest in the jazz scene and made the last of many appearances at the Ealing jazz festival in 2003, guesting with a group led by his bassist son Tommy McQuater Jr.
- In his later years, he concentrated his energy and playing around the Ealing Jazz Festival.
- After emerging from the heyday of the big bands as one of its most admired instrumentalists, he went on to become a successful session player, at home in every musical genre.
- He was a Scottish jazz trumpeter.
- In 1934, aged 20, McQuater was offered a job with one of London's most renowned bands: the Jack Payne Orchestra, which played in London and Paris. The following year he joined Lew Stone's band and made the classic recording of "Pardon Me, Pretty Baby".
- McQuater showed musical talent from an early age. Largely self-taught, he began on the cornet and by the age of 11 was a regular member of the Maybole Burgh Band - a brass band that won several competitions in the late 1920s - and played at local events and dances.
- He was also active as a teacher, helping top professional trumpeters such as Kenny Baker and Derek Watkins to iron out technical difficulties, also assisting Digby Fairweather and Alan Elsdon along the way. It was the latter who remembered that McQuater, known for taking the occasional nip of Johnnie Walker's Black Label, advised a glass of "Dr Bell's" as the answer to stage nerves.
- He also teamed him with another Scot, the innovative trombonist George Chisholm, cementing a personal association that continued until Chisholm's death in 1997.
- McQuater's studio work included jingles, movie soundtrack sessions - including the Carry On films - and had recording dates galore.
- McQuater toured and recorded with Benny Goodman's British orchestra in 1969, accompanied Frank Sinatra and Ella Fitzgerald, and played with everyone from Hayes to George Melly in a recording career that ran for half a century.
- He made a brief on-screen appearance in the 1962 thriller All Night Long, alongside Tubby Hayes, John Dankworth, Dave Brubeck, Charlie Mingus and a host of other eminent jazzmen.
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