Britain remained open to talks with the United States on how to address concerns about Iran.
Johnson wrote in his article that British businesses should cut all trade ties with Iran and help the U.S. form a "united front".
"It is clear that the danger from Iran did not diminish in the wake of the deal", he said.
Ambassador Robert Wood Johnson wrote in the Sunday Telegraph that "we are asking global Britain to use its considerable diplomatic power and influence and join us as we lead a concerted global effort towards a genuinely comprehensive agreement".
Iraqi Prime Minister Haidar al-Abadi's visit to Iran has been canceled after he said he had no choice but to abide by US sanctions against Tehran, even though he disagreed with their imposition.More news: Looking to live in Greece? Love cats? Click here
Al-Hamdani told the Iraqi website that the recent U.S. sanctions on Iran have not affected the Iraq-Iran trade relations, because "no steps have been taken by us and trade continues as in the past and has not been affected until now". "It is time to move on from the flawed 2015 deal", he said.
"We don't support the sanctions because they are a strategic error, but we will comply with them", said Abadi, whose country is an ally of both Tehran and Washington.
"Can I, the prime minister of Iraq, endanger the interests of Iraqis just to take a stand?" he said.
The US position was further undermined by an unnamed United Kingdom minister who accused Trump of simply throwing "red meat" to his support base, calling the sanctions strategy counter-productive, according to the Telegraph.
Britain's May might face a party leadership challenge later in the year, possibly from Boris Johnson, the former foreign minister who says she should be more like Trump. In June during the acrimonious G-7 meeting, held in Charlevoix, Quebec, which broke up amid highly personal recriminations between Trump and fellow summiteers over trade tariffs, May appeared especially eager to keep a low profile.
The comments come days after Mr Trump revealed new sanctions.