Houghton joined Chelsea's academy at Under-8 and has been with the club his entire career. In November 2014, he signed his first professional contract which will therefore keep him at the club until the end of the 2016–17 season.
On 20 July 2015, Houghton signed for League One side Gillingham on loan until 3 January 2016. On 8 August 2015, he made his professional debut in a 4–0 home victory against Sheffield United, playing the full 90 minutes. After establishing himself in the starting 11, Houghton scored his first professional goal in a 5–1 victory over Fleetwood Town on 29 September, also at Priestfield Stadium. On 2 January 2016, Houghton announced via his social media accounts that Gillingham had decided against extending his loan and that he would return to Chelsea after failing to impress under manager Justin Edinburgh.
On 10 March 2016, Houghton signed for League Two side Plymouth Argyle on loan. Two days later, he made his "Pilgrims" debut in a 2–1 away defeat to Accrington Stanley, playing the full 90 minutes. On 25 March, he scored his first Plymouth goal in the 14th minute of a 2–0 away victory against Morecambe.
On 6 August 2016, it was announced that Houghton will join Doncaster Rovers on loan until 3 January 2017. After the loan move was completed, Houghton made his debut as he started against Accrington Stanley in a 3–2 loss. His loan deal was extended till the end of the season on 1 January 2017. On 1 January 2017, the loan deal got extended once more, this time until 31 May 2017. On 21 February 2017, Houghton's loan spell was terminated after the midfielder suffered a knee injury during Doncaster's 1–1 draw with Luton Town on 18 February. On 31 August 2017, Houghton returned to Doncaster on loan until 3 January 2018. Two days later, he made his Doncaster return during their 0–0 draw with Peterborough United, replacing Niall Mason in the 59th minute. On 5 January 2018, Houghton's loan spell at Doncaster was extended until the end of the campaign.
On 6 July 2018, following his release from Chelsea, Houghton signed for League Two club Milton Keynes Dons on a two-year deal. He scored his first goal for the club on 27 October 2018, a long range strike in a 1–1 draw away to Mansfield Town.
