Barrow taught mathematics to the son of Sir George Leonard Staunton; through Staunton's interest, he was attached on the first British embassy to China from 1792-94 as comptroller of the household to Lord Macartney.
Barrow ceased to be officially connected with Chinese affairs after the return of the embassy in 1794, but he always took much interest in them, and on critical occasions was frequently consulted by the British government.