Mr Bullock, who was leader of Lewisham LBC between 1988 and 1993, will seek the Labour nomination, while Lewisham leader David Sullivan, has confirmed he will also seek the nomination.
Mr Sullivan, who is director of Millwall Football Club, said: 'If an election happens, I'm the leader of the council and would like to continue as the mayor.'
Joan Ruddock, local MP and chair of the Lewisham says Yes campaign, denied she would seek nomination. She said she was 'absolutely not' interested.
He worked for the Greater London Council for 10 years, including a stint as a policy assistant to Ken Livingstone developing the Fares Fair policy. He later joined Capita as a consultant and trainer.
Lewisham's mayoral referendum is taking place on 18 October. Conservative Party vice chairman and former London mayoral candidate Steve Norris has given his backing to the Yes campaign.
Mr Norris said: 'The great majority of decisions councils have to make are not political. They are executive and administrative.
'For the sake of the community as a whole, they should be taken quickly and effectively by a single accountable individual elected on a clear mandate to produce results.'
Former Brighton & Hove Council leader and local Yes campaigner Lord Bassam, who returned from holiday this week, was keeping a low profile.
He was unavailable for comment on whether he would seek the Labour nomination in the event of a mayoral election for Brighton & Hove, although a strategy document by him on the campaign has been leaked (LGC, 10 August).