Brengola was born in Naples. A child prodigy, he made his first studies with his father, and got his violin diploma in the Casablanca Conservatory at the early age of 11. returning to Italy, he studied violin with Arrigo Serato and orchestral conducting with Paul van Kempen in Bologna. He won the Geneva Violin Competition in 1936 and was finalist on the first occasion of the International Eugène Ysaye Competition, Brussels, together with David Oistrakh, Ricardo Odnoposoff (de) and others. Between 1939 and 1966 he was first violin and leader of the Quintetto Chigiano, and later of the Sestetto Chigiano.
In his long and successful career he performed extensively around the world (in Europe, Asia and America) with these groups. He also appeared as a soloist with such illustrious conductors as Sergiu Celibidache, Antonio Guarnieri, Carlo Maria Giulini, Igor Markevitch, Jonel Perlea, Paul van Kempen, Erich Leinsdorf, etc., and with other equally famous instrumentalists including Andrés Segovia, Alain Meunier and Dino Asciolla.
He was emeritus Professor at the Accademia Musicale Chigiana of Siena for 64 years, an academic of Santa Cecilia and titular professor of Musical achievement at the Accademia Nazionale di Santa Cecilia in Rome. Brengola was a close friend of the famous Bolognese violin maker Ansaldo Poggi and played his violins on a number of occasions. He also owned superb instruments: the Giovanni Battista Guadagnini 1747 violin known as 'Contessa Crespi'; the 1702 Antonio Stradivari 'Conte di Fontana' violin which had belonged to David Oistrakh and is now played by Massimo Quarta; and an excellent Roberto Regazzi instrument made in the 1980s.
He is regarded as one of the finest Italian violinists and violin teachers of the 20th Century. Among his many students a special mention goes to Luca Ciuffoletti, a violinist that developed an international career and that was one of Brengola's most affectionated student. In addition to his Decca recordings with the Quintetto Chigiano (see article for listing), in maturity he also recorded the Brahms violin sonatas with the pianist Piernarciso Masi. He died in Rome.