Delamere is from Edenderry, County Offaly. He has a degree in Computer Applications from Dublin City University (DCU), where his portrait is displayed in the university's library amongst other famous graduates. He began his career in 2004 at the Edinburgh Festival. Since then he has worked for both Raidió Teilifís Éireann (RTÉ) and the BBC, in programmes such as the BBC comedy series One Night Stand, BBC radio and television panel quiz The Blame Game and RTÉ topical comedy show The Panel. He hosts Neil Delamere's Just For Laughs, a comedy television show in which he interviews acts performing at the Montreal Festival. He featured on Michael McIntyre's Comedy Roadshow on 4 July 2009. Delamere made his debut appearance on Radio Five Live's Fighting Talk, broadcast on 11 December 2010, when he won the panel show. Since his first appearance on the show, Delamere has made several appearances on the Sony Award Winning Sports Show.
In 2011, he hosted The Only Viking in the Village on RTÉ, in which he explored his Viking roots and informed viewers that the Vikings poured urine on their clothes. The show was nominated in the factual category for an Irish Film and Television Award, and won. He has stood in for John Murray on RTÉ Radio 1.
He presented comedy documentary There’s Something about Patrick which aired on 14 March 2013 on RTE 1. In the documentary Delamere travels the length and breadth of Ireland (and beyond) to meet experts, historians and St Patrick’s Day revellers, to discover the truth about the Irish patron saint.