The UK's terrorism threat level has been lowered to severe after being raised to critical, its highest level, following Friday's attack on a London Tube train.
In the attack, a home-made bomb sent a wall of flames over commuters at Parsons Green on Friday, but apparently failed to detonate fully, injuring dozens of people.
A second man has also been arrested as part of the investigation into the attack.
The 21 year old was arrested in Hounslow, west London, on Saturday night on suspicion of a terror offence and is in custody in south London.
An 18-year-old man is also being held on suspicion of a terror offence over the Parsons Green explosion.
The 'severe' terror threat level means an attack is no longer imminent but is still highly likely.
Police are searching a residential address in Stanwell, Surrey, in connection with the 21-year-old man's arrest.
Home Secretary Amber Rudd said that over the next few days the military would return to their original positions.
She said the police had made "good progress" in the investigation but urged "everybody to continue to be vigilant but not alarmed".
Assistant Metropolitan Police Commissioner Mark Rowley said police had gained a "greater understanding" of how the bomb was prepared but said there was "still much more to do" in the investigation.
Of the 30 people injured in Friday's attack, one remains in hospital, NHS England said.
Ms Rudd said there was "no evidence" to suggest Islamic State were behind the attack, although the terrorist group has claimed responsibility.
"But as this unfolds and as we do our investigations, we will make sure we find out how he was radicalised if we can," she said.
Defence Secretary Michael Fallon said internet giants such as Google, Microsoft and Facebook, were not doing enough to help in the fight against terrorism.
On a trip to Qatar, Sir Michael said they need to "take down information that allows terrorists to construct the sort of device we saw on the tube".
Police are continuing to search a house in Sunbury-on-Thames in Surrey.
It is thought the 18-year old, who was arrested in the port of Dover on Saturday morning, lives there.
The BBC's home affairs correspondent Dominic Casciani, who was at the scene, said a large number of officers have been working inside the property and a forensics tent is in place in the back garden.
The house belongs to an elderly couple known for fostering hundreds of children, including refugees.
Ronald Jones, 88, and Penelope Jones, 71 were rewarded for their service to children when they were made MBEs in 2010.
The couple are said to be staying with friends following the police raid, during which surrounding houses were evacuated.
Shadow Home Secretary Diane Abbott raised concerns about police resources amid a rise in terrorist attacks.
She said cuts in policing have "possibly jeopardised our ability to respond to terrorism".
But Ms Rudd said the government was "committed to making sure the security services and the police have the right resources".
She announced £24m of funding for counter-terrorism operations across the country.
And she said that US President Donald Trump's suggestion that the terrorist behind the attack was "in the sights of Scotland Yard" was "pure speculation".