The men included a 27-year-old man arrested in Ilford on June 9, a 28-year-old man arrested in Barking on June 10 and a 19-year-old man arrested in Barking on June 11, the Metropolitan Police said in a statement posted on its website.
The police said that a 33-year-old man arrested in Ilford on June 8 is the only man to have been bailed to date.
Another 17 have previously been released without charge in connection with the attacks earlier in the month in which eight people were killed and 50 injured after three Islamist militants drove into pedestrians on London Bridge and stabbed people at nearby restaurants and bars.Islamic State, which is losing territory in Syria and Iraq to an offensive backed by a U.S.-led coalition, claimed responsibility for the incident which was the third militant attack in Britain in less than three months.