Wilmot joined Stevenage as an academy scholar, and progressed through the youth ranks at his hometown club. As a first-year scholar, he signed his first professional contract with the club in April 2017, having impressed throughout Stevenage's FA Youth Cup run during the 2016–17 season. He made his first-team debut on 3 October 2017, playing the whole match in the centre of defence as Stevenage drew 0–0 away at Milton Keynes Dons in the EFL Trophy. He established himself as a first-team regular throughout January 2018, helping the club keep three clean sheets in six matches. Stevenage chairman Phil Wallace stated the club had rejected three bids from Premier League clubs for Wilmot during the 2018 January transfer window, which included a £500,000 bid from Watford, whilst Tottenham Hotspur offered "slightly less". Wilmot was not included in any of Stevenage's matches from the start of April 2018 until the remainder of the season with a transfer "close" to being agreed. He made 15 appearances during the campaign.
Watford
Wilmot signed for Premier League side Watford on 24 May 2018, for an undisclosed fee and on a five-year deal. Stevenage stated that the fee was a record transfer fee received by the club and that it could rise significantly based on Wilmot's future appearances. Wilmot made his first-team debut for Watford in the club's EFL Cup tie away at Reading on 29 August 2018, starting and playing the whole match in a 2–0 win.
Loan to Udinese
Wilmot joined Serie A club Udinese on loan on 31 January 2019 for the remainder of the 2018–19 season. He made his Udinese debut in the club's 4–1 loss away to Juventus on 8 March 2019, playing the first half of the match. Wilmot made five appearances for Udinese during the loan spell.
Loan to Swansea
Ahead of the 2019–20 season, on 25 July 2019, Wilmot joined Championship club Swansea City on a season-long loan deal. He made his Swansea debut in the club's 3–1 home victory over Northampton Town in the EFL Cup on 13 August 2019, playing the whole match. Wilmot made just two appearances in the opening two months of the campaign, eventually making his Championship debut as an late substitute in a 2–1 away win at Charlton Athletic on 2 October 2019. He scored his first goal for the club in the South Wales derby; his first-half header proved decisive in an eventual 1–0 victory on 27 October 2019.
International career
Wilmot was called up to represent England U19s in March 2018 for their three 2018 UEFA European U19 Championship qualification matches in Skopje. Wilmot was the only player outside of the top two divisions to be named in the squad. He made his England U19 debut in a 3–0 win over Latvia U19s on 24 March 2018, coming on as an 84th-minute substitute in the match. In doing so, he became the first Stevenage player to represent England at youth level. Wilmot was included in the England U21 squad on 30 August 2019. He was called up once again in October 2019 and eventually made his U21 debut in a 2–2 draw against Slovenia U21s in Maribor on 11 October 2019, coming on as a second-half substitute in the match.
Style of play
Described as a "ball-playing midfielder" in the youth system at Stevenage, Wilmot moved into central defence where he was deployed during his breakthrough season in the first-team with the club. After signing for Watford, manager Javi Gracia stated that Wilmot "has the intelligence" to play in a holding midfield role in front of the two central defenders. He was subsequently deployed there during the 2018–19 season for both Watford and Udinese. Wilmot considers himself primarily a defender, but states he is also comfortable playing in midfield. He has said he does not model his game on any other player, but "takes inspiration from technically-gifted players" such as Sergio Busquets.
Personal life
He is the son of former Stevenage goalkeeper Richard Wilmot, who made over 150 appearances for the Hertfordshire club.