The bomb, found by contractors at a building site in Bethnal Green area of the city yesterday afternoon, was thought to have been dropped during German bombing raids in the early 1940s but did not detonate, according to the London Fire Brigade.
Families spent the night in a school hall in a Bethnal Green Academy where a rest centre was operational.
A police hazard zone cordon was extended to 200 metres, leading to families being evacuated to a Tower Hamlets Council rest centre.
"We do have an operating rest centre at the Bethnal Green academy - where we will be providing beds, food, drinks, and wash bags," a council spokesperson said.
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Army's bomb disposal experts have been working overnight to try and defuse the bomb.
The UK's Ministry of Defence (MoD) confirmed a bomb disposal team from the Royal Logistics Corps was on the site and assisting police.
Earlier this year, the squadron defused similar historic bombs in Bermondsey, south London, and Wembley, north London.