Bleakley runs for the Westminster seat of Belfast East in 1970 (gaining 41% of the vote), February 1974 and October 1974 for the Northern Ireland Labour Party each time, but never enough to win the Westminister seat from the Ulster Unionist Party (UUP). In 1971, Brian Faulkner appoints him as his Minister for Community Relations at Stormont, but as Bleakley is not an MP, he can only hold the post for six months. He resigns five days before his term expires in order to highlight his disagreement with government policy, specifically the failure to widen the government to include non-Unionist parties, and the decision to introduce internment. He writes a respectful biography of Faulkner and his own memoir of the period.