Beauchamp was educated at Westminster School and Christ Church, Oxford and entered the British Army in 1803 as a cornet in the 13th Dragoons. Made a captain in the 16th Light Dragoons, Beauchamp served with the regiment during the Peninsular War from 1809 until its end in 1814. He took part in the First Battle of Porto and then in the Battle of Talavera. After the Battle of the Côa in 1810, he was wounded in the Battle of Bussaco. Beauchamp was promoted to major in the 1st Life Guards in 1815, to major-general in 1837 and received the colonelcy of the 10th Royal Hussars for life in 1843. Three years later he became lieutenant-general and finally general in 1853.