Born in Maidstone, Kent,[2] Pigott began his career with Charlton Athletic and was offered a professional contract in January 2012.

[6] His loan was extended by a further month on 27 February,[10] but was later recalled by manager José Riga on 24 March, having scored one goal from seven appearances for Gillingham.

[13] Pigott scored an equaliser from 30 yards into the top corner in a 1–1 draw at home to Accrington Stanley on 25 October, having entered the match as a 62nd-minute substitute.

[14] Newport manager Justin Edinburgh confirmed that Pigott would return to Charlton following the expiration of his loan spell as the club "couldn't afford to keep him".

[13] Upon his return to Charlton, Pigott made his first appearance of 2014–15 for the club as a half-time substitute in a 2–0 defeat away to Blackburn Rovers on 20 December.

[17] He debuted a day later in a 0–0 draw at home to Plymouth Argyle and scored his first goal the following week in a 3–2 win away to Oxford United.

[25] This marked the start of a run of five goals from four matches,[26] which saw him nominated for the PFA League One Player of the Month award for October.

[29] He scored his first two goals in a 3–2 win away to Oxford United on 16 April,[30] which saw him earn a place in the Football League Team of the Week.

[34] He debuted on the opening day of 2016–17 in a 1–1 draw at home to Barnet and scored his first goal in a 1–0 win away to Shrewsbury Town in the EFL Trophy on 30 August.

[35] However, Pigott struggled to force his way into the first team and was loaned to National League club Maidstone United on 27 January 2017 until the end of 2016–17.

[41] On 28 August, Pigott scored after 77 seconds in Wimbledon's EFL Cup match against Premier League club West Ham United, but was substituted after Rod McDonald was sent off later in the first half; the Dons went on to lose 3–1.