Twiddy started his career with English side Plymouth [Argyle F.C.|Plymouth Argyle FC]. In 1996, he signed for Irish side Sligo [Rovers F.C.|Sligo Rovers FC]. In 1997, he signed for Norwegian side Hønefoss BK. In 2000, he signed for Norwegian side Hamarkameratene. He was described as "gained the full trust of coach Cato Bakkemo, and is flourishing like never before" while playing for the club. After that, he signed for Norwegian side Skeid Fotball. In 2003, he signed for Norwegian side Kongsvinger IL Toppfotball. In 2004, he signed for Norwegian side Hamar IL.