As a child actor is took on the role of Oliver Twist in the original run of Lionel Bart's Oliver! and he is possibly best known for his role as Colin Russell in BBC TV's EastEnders – a character famous for being the first gay man to kiss another man in a soap opera in the UK. He also appeared in the ITV drama serial The Sandbaggers and the Doctor Who story "Time-Flight".

Cashman is open about his homosexuality and regularly comments on government policy decisions relating to sexual orientation. He registered a civil partnership with Paul Cottingham, his partner of over twenty years, on 11 March 2006. Cashman is an Honorary Associate of the National Secular Society and a Patron of The Food Chain, a London-based HIV charity.

In the European Parliament he is Labour spokesperson on human rights. He is the treasurer of Equity and led the campaign to obtain pension rights for members. His domestic partner is Paul Cottingham.