The arrests were made as security - along with Brexit - became the dominant issue for the 46 million eligible voters who cast their votes today in the general election in the UK.
Two men were arrested last night on a street in Ilford, the Metropolitan Police said.
A 27-year-old man was arrested on suspicion of the preparation of terrorist acts, while a 33-year-old man was held on suspicion of possession with intent to supply controlled drugs.
With that, 17 people have now been arrested in connection with the attack on Saturday that killed eight people and wounded several. Five remain in custody, the police said.
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A video in the British media showed armed policemen encountering the terrorists, who drove into pedestrians on London Bridge and then stabbed people in the nearby Borough Market.
The CCTV footage shows the three terrorists - Pakistan- born Khurram Shazad Butt, Moroccan-origin Rachid Redouane and Moroccon-Italian Yousef Zaghba - cornering a pedestrian and about to stab him before charging at armed police officers.
The video emerged as families of the London Bridge attackers expressed disgust over the massacre and distanced themselves from the extremists, saying the atrocity left them shocked.
Charisse O'Leary, who married Redoaunein Dublin in 2012, said she has "shed many tears for the people caught up in this horrific incident".
"I am deeply shocked, saddened and numbed by the actions of my ex-partner who has killed and injured so many innocent people. We have a beautiful young daughter, that for the last six months has been our only bond and reason for contact.
"My thoughts and efforts now are with trying to bring up my daughter with the knowledge that some day I will have to try and explain to her why her father did what he did," she said.
Separately, the Met Police made three further terror- related arrests in London, which, it said, were not related to the London Bridge attack." They have been taken into custody at a south London police station and are detained under the Terrorism Act," the police said.
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