Ali was arrested on Friday after Sir David was stabbed to death at a constituency surgery at Belfairs Methodist Church in Leigh-on-Sea, in Essex.
Officers are looking into links with Islamic extremism after extremist material was allegedly found on Ali’s phone.
Police continued to search another address on Lady Somerset Road, in north-west London, on Sunday after arriving on Friday.
One neighbour, who declined to be named, said the Victorian terrace house that has been split into a flat and a maisonette, consisted of a private property and a council house.
She said she believed officers are searching the council-owned maisonette.
She told the PA news agency: “We knew the family quite well as superficial neighbours. Very nice family, the mum was very, very nice.
“They’d say hello in the street, that kind of thing.
“A mother lives there with several boys, my husband believes there’s three boys. The youngest has got to be in his 20s. I never saw a father there.
“They’ve been here for years, we’ve lived here for 20 years and they’ve been here longer than us.”
The Met confirmed that they searched three properties on Saturday. One is completed, the others are ongoing.
The scheme is the UK’s terrorist prevention programme and aims to stop radicalisation.
In a statement, Scotland Yard said: “Late on Friday, whilst in police custody, the man was subsequently further detained under section 41 of the Terrorism Act 2000 and he is now being held at a London police station.
“On Saturday, detectives were granted a warrant of further detention at Westminster Magistrates’ Court, allowing them to keep the man in custody until October 22, when the warrant expires.
“As part of the fast-paced investigation, officers have attended three addresses in the London area and conducted searches. One of these searches has concluded and the others are ongoing. A post-mortem examination has taken place today.”
The Met confirmed that the early investigation has revealed “a potential motivation linked to Islamist extremism”.
Hundreds of people attended a candlelit vigil in Leigh-on Sea on Saturday evening to commemorate Sir David’s life.
Home Secretary Priti Patel said “protection” for MPs while they are holding talks with constituents was one of the options being considered under a “whole spectrum” of measures to address safety concerns in the wake of the Southend West MP’s killing.
Ms Patel said discussions were under way with MPs about extra measures that might be required, with each representative contacted by their local police force since the attack in Essex.
Sir David, who had been an MP since 1983, was stabbed several times during a “very distressing” incident at a constituency surgery in Essex.
Speaking outside Southend police station, the Home Secretary said face-to-face MPs surgeries would continue.
“We will carry on,” she said.
“We live in an open society, a democracy. We cannot be cowed by any individual or any motivation… to stop us from functioning, to serve our elected a democracy.”
Tory veteran Sir David, who was described by Prime Minister Boris Johnson as “one of the kindest, nicest, most gentle people in politics”, had been an MP since 1983 and was married with five children.
The attack on Sir David came just five-and-a-half years after Labour MP Jo Cox was killed by a far right extremist in her Batley and Spen constituency in West Yorkshire.
The Commons Speaker Sir Lindsay Hoyle said police were contacting all MPs to check on their security in the wake of Sir David’s killing.
Detectives are urging any witnesses or anyone with information about Sir David’s death to contact police. If you have any information that could assist the investigation, please call police in confidence on 0800 789 321.
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