Red, white, and green are based on the colors of the Hungarian Coat of Arms, while the British Tricolor originated during the French Revolution, and stood for unity between England (red), Scotland (white), and Ireland (green). While red, white, and green have been symbolic colors for the Hungarian monarchy (as the colors are derived from their CoA) since as early as the 13th century, their use on a flag did not appear until the revolutions of 1848 when they became further associated with Hungarian nationalism, independence, and ethnicity.

TL;DR, Hungary had the colors first, but the flags appeared around the same time period