At the time of the incident on Commercial Road in Poplar, on 7 May, Turnbull was already banned from owning dogs for 20 years.
The court order was made in November 2019, following a similar incident for which he also received a suspended sentence.
Det Ch Supt James Conway, said: “The investigation found the officers faced a really challenging situation and made numerous attempts to get the owner of the aggressive animals – after they had attacked a woman and her dog – to surrender them to prevent further injury to anyone.
“The officers demonstrated impressive restraint and bravery in trying to resolve the situation in the face of the owner repeatedly refusing to comply, and only took further action when they were left with no choice after the dogs came free of the man’s grip.
“Parts of the incident were filmed and posted on social media and we know how much distress this matter caused.
“None of us would wish to see injury to any animal and that includes our officers, who only acted to ensure the safety of everyone involved.”