British-born Abedi, 22, blew himself up on Monday night at the Manchester Arena indoor venue at the end of a concert by USA pop singer Ariana Grande attended by thousands of children and teenagers. She said he had been known to security forces "up to a point".
Almost 1,000 soldiers are on patrol, supporting police at key locations.
Britain's official terror threat level was raised to "critical", the highest level, late on Tuesday, meaning an attack was expected imminently.
A spokesman for the 23-year-old singer announced the decision on Wednesday evening following widespread speculation that dates would be affected.More news: 1 person dead after contracting botulism from gas station's nacho cheese
Heavily armed police raided an apartment building in Manchester on Wednesday afternoon and a controlled explosion was heard.
"If that's something that we did, I think that's a real problem", he said.
Across London, troops fanned out and authorities reconsidered security plans.
"(The goal) is to make our city as hostile an environment as possible for terrorists to plan and operate", said London Police Commander Jane Connors.
Chelsea soccer club said it had cancelled a victory parade that had been scheduled to take place on Sunday to celebrate its Premier League title. The elder Abedi denied that he was part of the militant group and told The Associated Press that his son was not involved in the concert bombing and had no connection to militants.More news: Mueller Cleared by DOJ Ethics Experts to Lead Russia Probe
British authorities were also exploring whether the bomber, who grew up in Manchester, had links with other cells across Europe and North Africa, according to two officials familiar with the case who spoke on condition of anonymity because they were not authorized to speak about the ongoing investigation.
He said the man used to wear traditional white Islamic dress, was aged in his 20s, 6 ft. He said the man is named Adel and is in his 40s, with a wife and several children.
'I've been friends with Ariana Grande's family for many, many years. "I haven't seen police come to his house". He spent 25 years in Britain before returning to Libya after Gadhafi was ousted and killed in the country's 2011 civil war.
He said, however, that even if USA intelligence sources shared vital information with the media, it likely would not affect the strong intelligence sharing relationship between the US and Britain because it helps both countries.
Home Secretary Amber Rudd has also expressed concern that Abedi may not have been working alone.More news: Manchester attack probe widens; United States leaks spark anger
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