Career
Hartlepool United
Baldwin was on trial at Gillingham and impressed Gills boss Andy Hessenthaler after a season with Faversham Town"s first-team at the age of 18 years before going on trial with North-East side Hartlepool United and signing a professional contract after impressing manager Mick Wadsworth in pre-season friendlies. Prior to signing this contract, Baldwin was due to start University in a few months time to do a course in Sports Therapy at Kent. Baldwin made his senior debut for Hartlepool United on 17 December 2011 in a 1–0 home defeat against Colchester United with caretaker boss Micky Barron saying "Jack came in and was steady.
He"s been terrific since he came to the club on trial in pre-season."
At the end of the 2011/12 season, Baldwin committed his future to Hartlepool by signing a long-term contract with the club
Peterborough United
Baldwin moved to League One side Peterborough United for £500,000 on 31 January 2014 just minutes before the transfer deadline. On the 1st of November 2014 Baldwin captained Peterborough for the first time.
In the same game he ruptured a knee ligament that would rule him out for the next ten to twelve months. Baldwin is a versatile football player who can play centre-back, right-back or central midfield.
Former Hartlepool manager Neale Cooper likened 18-year-old Baldwin to a "young Alan Hansen" praising Baldwin on "the way he reads the game".