Kok was born in Brakpan in South Africa in 1924; his father, once a farmer, was a miner, and his mother played violin and piano.
The family moved to Britain in 1938, and he attended Haberdashers' Aske's Boys' School; with a scholarship, he went to the Royal Academy of Music, studying with Rowsby Woof.
In 1947, with his brother the cellist Alexander Kok, and pianist Daphne Ibbott, he formed the Beaufort Trio.
He was sometimes guest leader of the Boyd Neel Orchestra; the violinist Peter Mountain said "We always enjoyed his leading – he led firmly and his playing had strength and truthfulness".
[1][2] He joined the Philharmonia Orchestra, where the conductors he played under included Herbert von Karajan, Otto Klemperer and Wilhelm Furtwängler.