Born in Saddleworth in the West Riding of Yorkshire, Rhodes was educated at St Mary's School, Greenfield, and Huddersfield Technical College.
During the Second World War, Rhodes, by then a mill-owner and Chairman of the Saddleworth Urban District Council, became the commanding officer of his nearby Local Defence Volunteers (LDV), formed in 1940 to defend Britain against the armies of the Third Reich, then in occupation of much of Northern Europe and having succeeded in expelling the British Expeditionary Force from Europe at Dunkirk.
The name was quickly changed to the Home Guard and within a few weeks was equipped with rifles, army pattern khaki uniform and had officers and NCOs appointed.
A few months later he was elected as Member of Parliament for Ashton-under-Lyne in a by-election on 1 October created by William Jowitt's elevation to the peerage.
He was created a life peer on 14 September 1964 as Baron Rhodes, of Saddleworth in the West Riding of the County of York.
He was made a Privy Counsellor in 1969, a Knight Companion of the Garter in 1972 and served as Deputy-Lord Lieutenant of Greater Manchester from 1974.