The UK's threat level has been lowered from 'critical' to 'severe' after two people were arrested in connection with the terror attack at Parsons Green Tube station.
Home Secretary Amber Rudd said police had made "good progress" in the investigation as she announced the decision to downgrade the threat assessment from the highest alert level.
The terror threat level from international terrorism is back down to 'severe' - the same as Northern Ireland-related terrorism.
The PSNI said it had stepped up patrols in Northern Ireland, "particularly around iconic sites, transport networks, and where large numbers of people congregate", in response to the London attack.
Meanwhile, CCTV images have emerged which appear to show a person carrying a Lidl shopping bag on the morning of Friday's rush hour Tube attack.
The footage, acquired by ITV News, is reported to have been filmed near a house in Sunbury-on-Thames, Surrey, which is at the centre of one of two police raids.
Images posted on social media following the Parsons Green attack appeared to show wires protruding from a flaming bucket inside a plastic Lidl carrier bag on the floor of a train carriage.
An 18-year-old man, understood to be the suspected bomber, and a 21-year-old man remain in custody after being arrested by police on Saturday.
Assistant Commissioner Mark Rowley, the country's top counter-terrorism officer, said developments in the operation had provided "greater clarity" on the attack.
He added: "We are getting a greater understanding of the preparation of the device.
"There is still much more to do but this greater clarity and this progress has led JTAC - the independent body that assesses threat - to come to the judgment that an attack is no longer imminent."
The 18-year-old man was detained on Saturday morning in the departure area of Dover ferry port, which is the busiest ferry hub in Europe and a gateway to the French coast.
Police are continuing to search a house in Sunbury-on-Thames - home to Penelope and Ronald Jones, aged 71 and 88 respectively, who previously received MBEs for services to children and families. Dave Solway, who lives opposite Mr and Mrs Jones, said he saw the property being "swarmed" by police during Saturday's raid.
The 44-year-old said: "Counter-terror police began banging on their front door with shields, bomb-proof shields.
"I saw Penny being pulled out, basically; I didn't see Ron, don't know if he was there. There was loads of them, it was swarmed, there must have been a good 15-20 easily round the back, front, side of the house."
Mr and Mrs Jones, who have been foster parents for almost 40 years, had taken in up to 300 children during that time, including eight refugees.
A local politician said he understood an 18-year-old who had lived with the couple to be an Iraqi orphan who had moved to Britain, aged 15, after his parents died.
Thirty people were injured when the improvised device exploded during Friday morning rush hour at Parsons Green Tube station, with all but one now discharged from hospital.