The US is refusing to send back Anne Sacoolas, who was driving the car that hit the 19-year-old’s motorbike in August – but the prime minister has urged the president to think again.
Mr Johnson hinted at the demand at the weekend, when he said – after Ms Sacoolas was charged – that it was important that “the law should take its course”.
A government source told The Independent: “Of course we want her to come back. The PM has made that point to the president.”
Ms Sacoolas returned to the US after the collision, outside RAF Croughton in Northamptonshire, and subsequently claimed diplomatic immunity.
However, the Foreign Office then said her husband was not a registered diplomat and, on Friday, the Crown Prosecution Service (CPS) decided there was no immunity for dependants of consular officials.
It will now begin extradition proceedings through the Home Office, but the US may still reject the request on those grounds and the UK fears it could drag on for a long time.
On Friday, a spokesman for the US State Department said: “It is the position of the United States government that a request to extradite an individual under these circumstances would be an egregious abuse.”
And Amy Jeffress, Ms Sacoolas’s lawyer, said” “Anne will not return voluntarily to the United Kingdom to face a potential jail sentence for what was a terrible but unintentional accident.”
Instead, US officials have been negotiating to see if the Dunn family would allow the Sacoolas family to help provide a memorial for their son, as well as training to prevent similar accidents in future.
Mr Johnson’s intervention came when Mr Trump rang last week to congratulate the prime minister on his general election triumph.
The prime minister’s spokesman declined to confirm that he had pressed for extradition on the grounds that “this is a legal process now”.
He said: “The prime minister has discussed the case directly with President Trump on a number of occasions, including the last occasion on which they spoke.
“He said it’s important that the law should now take its course.
“This will be before the courts, but the PM has stressed on many number of occasions the importance of achieving justice for Harry’s family.”
However, the spokesman played down suggestions of Mr Johnson meeting Harry’s family imminently.
Since the investigation into the teenager’s death was launched, the family have taken their fight to the US and even met Donald Trump at the White House.
The meeting with the US president also sparked controversy after it later emerged that Ms Sacoolas was sat in the room next door ready to meet Mr Dunn’s parents – an offer the teenager’s family refused.