Before Acker became a musician he worked at the Bristol Wills Tobacco factory for £1.4s a week, and also dabbled in a little boxing. He married his childhood sweetheart Jean. Then, in 1948 he started playing the clarinet and whilst in the Royal Engineers in the Canal Zone, he borrowed a military clarinet and began to copy records. He was sent to the glasshouse for sleeping on duty and endured with the boredom by practicing. Demobbed, Acker formed his first band in Bristol, but soon moved to London to play with the Ken Colyer band. However, he hated London and moved back to Bristol and formed the Bristol Paramount Jazz Band. In 1951 the band played in London, and Acker and Jean had to survive living above a factory in Plaistow, until the band got their first big break - six weeks constant playing in a beer hall in Dusseldorf. This really disciplined the band, and they never really looked back. Hit Jazz records followed such as "Summer Set" and "Creole Jazz".

Then, in 1961, Acker recorded "Stranger On The Shore". This was an international hit, and the first ever record to be No.1 in the UK and US at the same time, although there is a slight dispute over the UK charts as there were so many different charts. In 2002, the year of the 50th Anniversary of the start of the Official UK Charts, Acker was delighted when "Stranger On The Shore" was acclaimed No.58 in the charts since they began.

He continued to perform until well into his 80s, although he reduced the number of live appearances to concentrate on one of his favorite hobbies, including painting.