The foreign secretary Dominic Raab has appealed directly to the American woman who drove the car that killed the motorcyclist Harry Dunn to return to the UK to face justice.

Speaking after his second meeting with the 17-year-old’s bereaved family, Raab said: “I appeal to Anne Sacoolas herself to do the right thing. If there is a charging decision from the Crown Prosecution Service (CPS), I urge her to come back to the United Kingdom and cooperate with the criminal justice process.”

Raab also said he would complete a change to the rules surrounding diplomatic immunity for staff that work at RAF Croughton, the airbase where Sacoolas’s husband worked.

She has admitted she was driving on the wrong side of the road after only a few weeks in the UK when she collided with Dunn’s motorbike in August, fatally injuring him.

Soon after the crash, the Donald Trump administration flew Sacoolas and her family back to the US claiming diplomatic immunity. News of her flight abroad was kept from the Dunn family for as long as 10 days.

Raab met Dunn’s family at the Foreign Office on Tuesday. The family are waiting to see if the CPS will bring some form of dangerous driving charge against Sacoolas. The Dunn family say they cannot start the grieving process until she has faced justice.

Relations between the family and Raab have been deteriorating over recent months as Dunn’s lawyers applied for judicial review over the Foreign Office’s decision-making process. The family are also seeking to start a legal action in the US against Sacoolas .

The Dunn family said Tuesday’s meeting with Raab had been much warmer and more helpful than their previous encounter, with the family spokesman Radd Seiger even claiming it was “the best day of the campaign so far”.

In a statement the foreign secretary said he appreciated the family’s pain and welcomed the chance to address their concerns. He added: “We are united in our determination to get justice for Harry. The government will do everything it can. I also reaffirmed my commitment to conclude the review of the arrangements at RAF Croughton by the end of the year to ensure they cannot be used in this way again .”

In a marked change in tone, Seiger described the meeting with Raab as a “warm, constructive and positive dialogue”, but trained his criticism on the delays in a charging decision by the CPS.

He said: “There is no good reason why it has taken them six or seven weeks to make a decision. Everyone in authority does not understand it. Lawyers and experts are all scratching their heads. The CPS will not engage with us.”

But he added he was “100% confident a charging decision is coming. We believe it is imminent. It is time. It is absolutely the time.”

He acknowledged that if the CPS sought to charge her, a “potentially complex drawn-out process lay ahead if Sacoolas, with the help of the US government, fought her extradition”.

Seiger said “The US has never ever turned down an extradition request from the UK and there is no good why this should be turned down.”

He reported that Raab had told them that he had spoken forcefully to the US secretary of state Mike Pompeo on the issue of extradition on the sidelines of the recent Nato meeting in London.

Sacoolas’s husband was an intelligence officer, and Pompeo, as a former head of the CIA, may be under pressure not to see her extradited or set some precedent about claims for diplomatic immunity.

But Seiger vowed “This campaign is not going to stop until Ann Sacoolas is back in this country facing justice.”