The Respect Party leader, who lost his seat as Bradford West MP last month, outlined a range of policies designed to clamp down on what he described as the “social cleansing” of the city.
Speaking at the Ethical Society in Holborn, he said he would make the “housing crisis” his main priority reports BBC.
He said house prices were driving people “further to the edge of London, literally and metaphorically”.
Mr Galloway, 60, first announced his intention to run for mayor last month, pledging to “build a city that benefits everyone, not just those dripping in gold”.
During the speech and question-and-answer session, Mr Galloway said he would compulsorily purchase residential properties left vacant for at least one year and he also pledged to tackle white-collar crime.
Mr Galloway described current mayor Boris Johnson as a “blond buffoon”.
On 7 May, Mr Galloway lost the Bradford West seat he took from Labour, his former party, in a 2012 by-election.
The seat was won by Labour’s Naz Shah by a majority of more than 11,000 following a bitter campaign.