Police are continuing to question two men on suspicion of terror offences following Friday’s attack on a Tube train in south-west London.
It comes as CCTV images emerged showing a man carrying a Lidl supermarket bag 90 minutes before the bombing.
An 18-year-old and 21-year-old are being held over the explosion, which injured 30 at Parsons Green station.
The UK terror threat level has been lowered to severe after being raised to critical, its highest level.
On Saturday, the 21-year-old, believed to be Yahya Faroukh, was arrested in Hounslow, west London and the 18-year-old was detained at Dover port.
Local council leader Ian Harvey said he understood the 18-year-old was an Iraqi orphan who moved to the UK when he was 15 after his parents died.
Police are searching two addresses in Surrey in connection with the arrests – one in Sunbury-on-Thames and another in Stanwell.
Mr Harvey, who leads Spelthorne Borough Council, told the Press Association it was “widely known” the 21-year-old was a former foster child who had lived at the property being searched in his ward of Sunbury East.
A third property in Hounslow has also been searched as part of the investigation, Scotland Yard said.
The BBC understands it is a Middle Eastern chicken shop called Aladdins in Kingsley Road.
The “severe” terror threat level means an attack is no longer imminent but is still highly likely.
Home Secretary Amber Rudd said police had made “good progress” in the investigation and 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”.
Analysis: No ‘all clear’ yet
By BBC home affairs correspondent Dominic Casciani
The lowering of the threat level is an important sign.
It means that intelligence chiefs have looked at the developing picture in the Met’s huge operation – and other threads we will never see, from perhaps MI5 and GCHQ – and concluded that detectives now have a good handle on what happened on Friday at Parsons Green.
Or, to put it another way, the threat level would not have been reduced if anyone within the counter-terrorism network still thought there was a bomber, or accomplices, on the loose.
This is not the same as an “all clear” – intelligence is only ever fragmentary.
Detectives now appear to have time on their side.
Providing they make evidential progress, they could conceivably hold both suspects for up to a fortnight before they have to charge or release them.
Speaking to the Andrew Marr Show on Sunday, Ms Rudd said there was “no evidence” to suggest so-called Islamic State was behind the attack.
“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.
Thirty people were injured – most suffering from “flash burns” – when a bomb was detonated on a Tube carriage at Parsons Green station.
The house being searched in Sunbury-on-Thames belongs to a married 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.
Friend Alison Griffiths said the couple had an 18-year-old and a 22-year-old staying with them recently.
She described Mr and Mrs Jones as “great pillars of the community”, adding: “They do a job that not many people do.”
Police have urged anyone with information to contact them and to upload pictures and video to the website www.ukpoliceimageappeal.co.uk or to call the Anti-Terrorist Hotline on 0800 789 321.
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