Brian was born c. 1960 in England, the son of parents who remain unnamed throughout the series. As a child, Brian showed a great interest and skill in the visual arts. When his mother visits in "Help" (incidentally, the only parent of the characters who appears on-screen), it is mentioned that Brian was never very close to his father as they never had anything to connect over. After moving away from his parents and into the Meteor Street flat, he began to lie and tell his parents that he was actually a lawyer.
When Brian became unable to afford his rent, he struck a 'deal' with Marsha, allowing him to stay in exchange for sexual favours, until his housing benefit came through. This is a running gag on the show; Marsha makes repeated advances to Brian that he very awkwardly rejects.
Brian first appears in "Beginnings", in which he is introduced as the downstairs neighbour of Tim and Daisy. In "Mettle" Brian gets an invitation to do an installation at the art gallery. In "Chaos" Brian's Star Wars code name is 'Chewie.'
In the second series, Brian and Daisy's best friend Twist begin a relationship. This begins to impede on his artistic ability, because, as Marsha puts it, he's "happy". In "Dissolution", Twist ends things with Brian as she feels the relationship is only about sex and she is bored of it. Brian is clearly devastated by the break-up, much more so than Twist.