Downes was born in Walsall, Staffordshire, where he began taking violin lessons from Arthur Hytch, a local teacher who, according to Downes, "taught me violin, fly-fishing, and a little about the stock market."
By the time he was 18, he was a violinist in the City of Birmingham Orchestra, and then played with the BBC Midland Orchestra, and at Scarborough.
He became a violist in the Henry Holst Quartet in 1931, conducted a semi-amateur orchestra in Walsall, led his own quartet, and, from the BBC Scottish Orchestra in Glasgow, moved to the Liverpool Philharmonic. From this last ensemble came the Philharmonia Quartet: Downes and Holst with Ernest Element and Anthony Pini. When the Philharmonia Orchestra was founded, Downes became a principal in it, and played with the orchestra until 1974.
He retired in Exmouth in his 80s.
Downes' notable recordings include Richard Strauss's Don Quixote, with cellist Jacqueline du Pr_, and two versions of Brahms's Op. 91.