They were detained after an armed raid in Barking, east London, the day after the van and knife rampage by three terrorists who were shot dead by police.
Scotland Yard said the investigation into the “horrific attack” at London Bridge and Borough Market was progressing rapidly with officers searching several addresses in the area.
The arrests in connection with the attacks came as Prime Minister Theresa May warned that Britain is in the grip of a spate of copycat terror plots and it emerged that an off-duty Metropolitan Police officer was among the 48 people injured by the terrorists.
The attackers brought carnage to the streets of the capital brandishing 12-inch knives, shouting “this is for Allah”.
Police were called at around 10.08pm on Saturday to reports of a vehicle striking pedestrians on London Bridge.
The white van then continued to drive to Borough Market. The suspects were confronted and shot by police at Borough Market within eight minutes of the first emergency call being made.
It was the third terrorist outrage to hit the country this year following the Westminster and Manchester attacks which all together have killed 34 people
Speaking outside Downing Street, Mrs May said that although there was no direct link between the three incidents: “As terrorism breeds terrorism and perpetrators are inspired to attack, not only on the basis of carefully constructed plots after years of planning and training, and not even as lone attackers radicalised online, but by copying one another and often using the crudest of means of attack.”
• A minute’s silence will be held at 11am on Tuesday in remembrance of those who died in the London Bridge attack, a Government spokesman said.
The silence will be marked at all government buildings and f lags will remain at half-mast on Whitehall government buildings until Tuesday evening.
• Dozens of Londoners and businesses are opening their doors to people stranded in the capital after the London Bridge attack by sharing offers on social media with the hashtag #SofaForLondon.
Nadine Stares said: “Sofabed available if you are stranded due to this sad incident at London Bridge #SofaForLondon”.
Another Twitter user who gave, his name as Ben Andrews, wrote: “If anyone is caught in London Bridge incident needs place to sleep, we have a spare room 10mins walk away from #London Bridge #sofaforlondon.”
The Makersville bike workshop in Hackney tweeted: “#sofaforlondon heads up guys - if you’re stuck, let us know.”
Members of the public have also been pictured bringing hot drinks and food to police at the scene.