The prime minister says he only learned of security concerns around the ex-US ambassador earlier this week.
Lebanon's health ministry says more than 300 people died in strikes on Wednesday.
Yvette Cooper said coordinated diplomatic and economic measures are required to reopen the shipping lane.
Iran's foreign minister urges his UK counterpart Yvette Cooper to end cooperation with the US.
The phone call comes after a week in which Donald Trump repeatedly expressed frustration at Keir Starmer's stance on Iran.
Foreign Secretary Yvette Cooper has hit back at President Trump's criticism of the UK response to the conflict in Iran.
Foreign Office sources say no evacuation was imminent but the government is preparing for potential scenarios.
The foreign secretary said the UK would "continue to look at co-ordinated action, including increasing sanctions on the Russian regime".
Some 42 sanctioned tankers has passed through the Channel since 11 January, a BBC Verify analysis finds.
