It would also allow in global inspectors in return for the lifting of crippling economic sanctions.
It followed a question about Britain's ambassador to the United States, Kim Darroch, who resigned in a furore over leaked memos.
The deal had been previously struck by Trump's predecessor Barack Obama and a leaked memo now claims that Trump may have taken the decision against Tehran just to spike the former US President.
The memos said rumours of "infighting and chaos" in the White House were mostly true.
Trump was hostile to the accord with Iran because it was "Obama's deal" according to the leaked diplomatic cable.
"They can't articulate any "day-after" strategy; and contacts with State Department this morning suggest no sort of plan for reaching out to partners and allies, whether in Europe or the region", Darroch wrote. He asked "owners, editors and publishers" to refrain from releasing any further information relating to the disclosures.
In his statement, Basu urged the person or people who leaked the memos to turn themselves in.
He did not believe the Trump administration would "become substantially more normal; less dysfunctional; less unpredictable; less faction riven; less diplomatically clumsy and inept".
The US President branded Sir Kim a "very stupid guy" and said his administration would no longer cooperate with him.
The government launched an internal Whitehall inquiry into the publication following the reports. In a letter to Simon McDonald, the permanent under-secretary at the Foreign and Commonwealth Office, he said it was "impossible" for him to continue as ambassador.
"The Metropolitan Police respects the rights of the media and has no intention of seeking to prevent editors from publishing stories in the public interest in a liberal democracy", Mr. Basu said Saturday.
The leak of the diplomatic cables - in which Sir Kim was critical of President Trump - led to a spat between the White House and Britain.
His rival, Mr Johnson, said it was correct the person responsible for the leak was "hunted down and prosecuted" but it was wrong for police to target the media.
"It looks prima facie as a clear breach of the Official Secrets Act", Sir Michael told the BBC Radio 4 Today programme.
A British police investigation into the leak of confidential diplomatic memos is raising press freedom issues, as police warned Saturday that United Kingdom media outlets might face a criminal inquiry if leaked documents are published.
The Mail on Sunday, which first obtained the trove of leaked memos, has not faced any legal repercussions for its decision to publish.
Earlier this week, Trump said the USA will "substantially" increase sanctions on the Iranian government in the latest escalation in his administration's "maximum pressure campaign" against the country.