Peel was named after Arthur Wellesley, Duke of Wellington, and was educated at Eton and Balliol College, Oxford.

In 1873 to 1874, he was patronage secretary to the Treasury, and in 1880, he became Under-Secretary of State for Home Affairs in William Ewart Gladstone's second government.

Throughout his career as Speaker, as the Encyclopædia Britannica Eleventh Edition noted, "he exhibited conspicuous impartiality, combined with a perfect knowledge of the traditions, usages and forms of the House, soundness of judgment, and readiness of decision upon all occasions".

Peel was also an important ally of Charles Bradlaugh, whose campaigns to have the oath of allegiance changed eventually permitted non-Christians, such as agnostics and atheists, to serve in the House of Commons.

However, the report was published in Peel's name and recommended that the number of licensed houses should be greatly reduced.