The borough’s political leaders warned Boris Johnson not to pursue a No Deal Brexit after he was named the next prime minister.
Mr Johnson won the Conservative Party's leadership contest with 92,153 votes compared to his rival Jeremy Hunt's 46,656.
But the 55-year-old faces a daunting in-tray at Number 10, including keeping his "do or die" promise to meet the looming Brexit deadline of October 31.
Poplar and Limehouse MP Jim Fitzpatrick said: "Like me, Boris voted for the prime minister's deal last time as did most Tories and a handful of Labour members.
"He'll need to do something to tweak the deal. It's clear he won't get a No Deal outcome through Parliament."
The Labour Party MP added that as a former mayor of London Mr Johnson knows Tower Hamlets well.
Mr Fitzpatrick said: "Whether that will account for any more assistance than we have been receiving - which has been massive cuts to the council's budget - remains to be seen."
Canary Wharf's Cllr Andrew Wood, leader of the Conservative group at the council, said Mr Johnson won a clear majority and mandate to replace Theresa May as prime minister.
"But he faces a range of problems not least how to deliver Brexit in a way that works for the United Kingdom as a whole," Cllr Wood said.
"Normal government has been suspended for some months now and as a country we need to re-unite and move on with confidence and optimism, Boris's touchstones.
"My personal opinion is that a No Deal exit would not be good for Tower Hamlets and my ward in particular and I hope that he will find another solution that respects the vote to leave," Cllr Wood added.
Liberal Democrats Cllr Rabina Khan said the weeks ahead would prove to be a testing time for Mr Johnson.
She urged him to remember in the Brexit negotiations that Tower Hamlets has attracted "huge investment" from the European Union.
The Shadwell councillor voiced a hope that he would present a unifying vision for the country following past remarks Mr Johnson made in the press about Muslim women.
Bethnal Green and Bow MP Rushanara Ali said: "Boris Johnson has put our country in jeopardy by committing to leave the EU under any circumstances, even if this means leaving with No Deal.
"A No Deal Brexit would be catastrophic for our economy, destroying jobs and livelihoods and compromising our security.
"I'm appalled that the Conservative Party has elected a man who is happy to sell the country down the river in order to become prime minister. God help us all."
The former foreign secretary, who was the favourite to win the leadership contest, will be appointed as prime minister tomorrow (Wednesday, July 24) by the Queen after Theresa May formally resigns from the office.
Mayor of Tower Hamlets, John Biggs, said: "With Boris Johnson as Prime Minister, the threat of a no-deal Brexit looms over the country, threatening serious economic and social impacts for our borough.
"As the hard Brexiteers prepare to run the country, it's more important than ever that we continue to push for a referendum on the final terms of any Brexit deal.
"Boris made pledge after pledge about new spending plans and in the face of nearly a decade of crippling cuts to public services, it's vital that we see extra cash put into our local councils, schools, the police and the NHS. Without urgent action from the new prime minister our public services face a very bleak future.
"On the other hand we should, without holding our breath, hope that his previous role in London will mean that he will have fewer reasons to not address the needs of places like Tower Hamlets. Let us see."
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