Born in Sheffield, South Yorkshire, Jameson progressed through the Sheffield Wednesday youth system. He was loaned to Conference North club Gainsborough Trinity during the 2008–09 season, where he made three appearances. He joined Northern Premier LeaguePremier Division club Ilkeston Town on loan later that season. Jameson signed a new one-year contract with Wednesday during the summer of 2009 before being loaned to Harrogate Town of the Conference North for one month on 9 October. His debut came a day later in a 2–2 home draw with Droylsden, and completed the loan spell with four appearances. He joined Northern Premier League Premier Division club Matlock Town for one month on 29 November 2009. The loan was extended for a second month, before Wednesday recalled him in January 2010 due to an injury. He made his debut for Wednesday on 20 November 2010 in a League One match away to Milton Keynes Dons which ended in a 4–1 win. He made his second appearance for the club in the reverse fixture at home on 5 February 2011, with the match finishing a 2–2 draw. Jameson extended his contract at the club to another two years on 24 May 2012, with manager Dave Jones saying he was likely to be loaned out in 2012–13. He joined League Two club York City on an emergency loan for the rest of the season on 7 March 2013, although he did not make any appearances for the club. Jameson joined Conference North club Stalybridge Celtic on a one-month loan on 29 November 2013. On 10 January 2014, he joined League One club Bradford City on loan until 11 February 2014.
Non-League
Jameson signed for Northern Premier League Premier Division club Buxtonin the summer of 2014, despite clubs from higher divisions showing an interest in signing him. He debuted on the opening day of 2014–15, in a 1–0 home defeat to Nantwich Town. In January 2015, Buxton were seeking a new goalkeeper, as Jameson had made a number of high-profile errors over 2014–15. In November 2015, he joined Handsworth Parramore of the Northern Counties East League Premier Division on a dual registration deal, in order to play more matches. He made his debut in a 3–2 home win over Hallam, in which he made an 89th-minute save described by The Star as "brilliant". This result meant Handsworth progressed into the last 64 of the FA Vasefor the first time. Despite missing much of the season through injury, Jameson joined the club permanently in June 2016, but left two months later when rejoining Northern Premier League Premier Division club Matlock Town.
Coaching career
Jameson has coached goalkeepers aged 8 to 16 at Sheffield Wednesday and is the head goalkeeper coach at the Pro Player Football Academy.