[2] Allcock won double gold at the 1980 World Outdoor Bowls Championship in Melbourne in the team event (Leonard Cup) and triples with Jimmy Hobday and the legendary David Bryant.

He won singles silver medal in the 1994 Commonwealth Games in Victoria, British Columbia, Canada.

[5][6] Allcock was appointed the bowls performance coach for the England team at the 2002 Commonwealth Games.

[13] Having been appointed a Member of the Order of the British Empire (MBE) in the 1989 New Year Honours for services to bowls, he was promoted to Officer of the Order of the British Empire (OBE) in the 2019 Birthday Honours for services to lawn bowls.

[14][15] Allcock has written several books on bowls, and released a series of instructional videos on the subject.