Here’s the representation of minorities in the British armed forces(excluding around 4000 Gurkhas) (https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/310468/quarterly_personnel_report_apr14.pdf)
Britain, according to wiki, is around 87% white. So minorities are 13% in population, and 7% in the army. Underrepresented, but not so egregious that it causes me to be suspicious of the British armed forces. British Muslims are ~4.5% of the population(wiki), and 0.3% of the armed forces(if the numbers quoted in this thread are correct). This set of facts does not immediately lead me to conclude that Britain is at fault in integrating its minorities, particularly the Muslim one, especially as related to serving members of its armed forces.