Hudspeth spent nineteen seasons at Newcastle, from 1910 to 1929. This makes him the joint longest servant for the club along with Billy McCracken. During his time at the club he became a popular figure amongst the fans and gained the nickname 'Old Surefoot' for his reliability. He captained the team from 1923 to 1926 but was demoted to vice-captain following Hughie Gallacher's arrival at the club. Hudspeth was also known for his ability to score penalties and twenty-five of his thirty-seven goals at Newcastle came from the penalty spot.
He is second only to Jimmy Lawrence for making the highest amount of appearances for Newcastle, taking part in 472 games. He also represented England at international level.