It would be no exaggeration to say that the jazz musician Franz Jackson was the last of the heavyweight swing-era tenor saxophonists. His gritty tone and energetic phrasing were heavily influenced by Coleman Hawkins and Ben Webster, and indeed he replaced Webster in such legendary bands as those of Fletcher Henderson and Roy Eldridge.

Jackson began playing professionally with the great boogie-woogie pianist Albert Ammon in 1928, and his subsequent career was one of the longest in jazz history as he was still working 80 years later until suffering a broken hip in April this year.

He recorded with numerous bands including those of Earl Hines and Lil Armstrong (former wife of Louis), beginning to make discs under his own name in 1940. As well as playing the tenor saxophone, he was also a skilled and dextrous clarinettist, and his records from the 1950s and 1960s with his own Original Jass All Stars and with Lil Armstrong, mainly demonstrate his work on that instrument, on which he rivalled the virtuosity of his one-time boss, the New Orleans master Jimmie Noone.

Latterly Jackson was a fixture on the Chicago jazz scene, seeming to defy the passing years as he outlived all his sidemen, first at a long residency at the Red Arrow club in the suburb of Stickney and later at the Old Navy Pier on the lakeside. He toured Britain several times as a soloist and earlier this decade was a frequent visitor to Europe in the Legends of the Swing Era package led by the British drummer Trevor Richards.

Franz R. Jackson was born in Rock Island, Illinois, and studied at the Chicago Musical College before getting his first professional break with Ammons. In the 1920s Chicago was the capital of the jazz world, so as he was growing up Jackson heard at first hand all the great names from King Oliver and Louis Armstrong to Jelly Roll Morton and Zutty Singleton. A proficient sight reader, he worked in the big bands of Cassino Simpson and Carroll Dickerson before starting the first of many periods in Roy Eldridge’s group in 1937. Recordings exist of his exuberant playing on such pieces as Eldridge’s Heckler’s Hop. With Fletcher Henderson the following year, Jackson learnt arranging at first hand from the man who was at that time supplying most of the written arrangements for Benny Goodman. The Henderson influence was strongly evident on Jackson’s own pieces, such as Coming Home which he wrote for Earl Hines in 1940.

After travelling to New York with Eldridge, he remained there for a while, making the first discs by his own “Jacksonians” featuring the vocals of his then wife Maxine Johnson. He was recruited to Fats Waller’s big band, but he found the outsize leader’s constant partying took its toll on his health, and, as he related on BBC Radio Three a few years ago, he accepted a job with Earl Hines at Chicago’s Grand Terrace club to “get some rest” after his hectic months with Waller.

In Hines’s band he worked alongside the bassist Truck Parham, who became a lifelong friend and colleague. As the new style of bebop took hold, Jackson was never out of work, his huge tenor sax sound being in demand from such swing leaders as Frankie Newton and Wilbur De Paris.

When times got tight for older-style players, Jackson toured US service bases with the veteran bandleader Jesse Stone, who was just beginning a new career as a rhythm and blues singer under the name Charles Calhoun.

In the 1950s Jackson returned to Chicago for good, deciding from then on to lead his own band in the city as he raised his family. This coincided with the traditional jazz revival, and he made a name for himself playing clarinet and singing highly entertaining versions of such songs as Bill Bailey and St James Infirmary to which he added his own topical lyrics.

In 1981, under the aegis of the British record dealer and critic James Asman, Jackson came to Britain for his first solo tour. On one session, organised by the Times jazz critic and bassist Alyn Shipton, he was reunited for the first time since 1941 with Fats Waller’s guitarist Al Casey. The music was excellent, but most of the band remember Jackson for his prodigious appetite. He’d begun the day in Scotland, where after a full breakfast at his hotel he had partaken of another on the train to London, followed by a three-course lunch. He was picked up from King’s Cross station as he polished off a full cream tea, and on arriving for the gig at Farnham Maltings, bolted down a couple of helpings of chili con carne before going on stage. Asked about his remarkable skill as a trencherman, he said: “When you’ve been on the road as long as I have, if it rains porridge you hold your bowl out!”

Jackson was to revisit Europe numerous times, but he was never happier than when in the company of the Legends of the Swing Era, alongside his old friend Parham, and such other players as the pianist Red Richards and trumpeter Doc Cheatham. He outlived them all, his extraordinary energy as a performer undimmed, to the extent that he played a continuous two-hour jam session last November to celebrate his 95th birthday. His son and daughter survive him.

Franz Jackson, jazz saxophonist and bandleader, was born on November 1, 1912. He died on May 8, 2008, aged 95