Bromet came to note as a rugby player when he represented Cambridge University and won a sporting Blue when he played in the Varsity matches of 1887 and 1888. In 1891, Bromet was chosen to represent the British Isles team on the first official tour of South Africa. Bromet was selected for two of the Tests, playing at centre in the Second Test at Kimberley and then as a forward in the Third Test in Cape Town. Both were victories for the tourists. In total Bromet played in 14 games and scored ten tries, including three in the biggest win over the tour, against Pietermaritzburg.