Mrs Charles, who stood in front of a large banner featuring a photo of her son, said she had travelled to London “to continue to raise awareness” of her son’s case with political leaders.
She added: “We also put out an email to Boris Johnson’s team just a couple of days ago to see if there was any possibility at all of just grabbing a couple of minutes with him and President Trump together.
“We had an email back to say that our email was having some attention and consideration, it’s probably just a standard email, but us as a family would not be able to give up the opportunity of being in London just in case they ever did ring and say we’ve got a few minutes.
“We don’t think it’s going to happen but we couldn’t sit at home just in case.”
Harry’s family are demanding that American Anne Sacoolas, 42, who allegedly collided with Harry’s motorbike then fled to the US after claiming diplomatic immunity, return to face justice.
The teenager’s family met with Mr Trump at the White House in October, with Mrs Charles describing the president as “gracious” and “welcoming”.
She added: “But it was quite evident within a couple of minutes of being in the Oval Office that he wanted us there to try and smooth things over as such and have us meet with Anne Sacoolas who was in the next room.
“He was probably hoping that we would just then go away and grieve.”
Mrs Charles said it was “upsetting” that the UK and the Queen were hosting Mr Trump while he was “harbouring” the suspect in Harry’s case.
Asked if she trusted the political leaders to discuss the case during Mr Trump’s visit to London, she said: “We don’t really trust any of them at the moment.
“We’ve been lied to I think on a few occasions… it’s extremely hard to trust anybody.”
She added: “We keep saying we’re open to dialogue, we will continue to be open to dialogue.
“We are very much hoping that we get something back from today, but what it will be and when it will be, your guess is as good as mine really.”
Earlier on Tuesday, a government spokesman said Foreign Secretary Dominic Raab, who has been criticised by the Dunn family for his handling of the case, raised the issue with US Secretary of State Mike Pompeo when they met in London.
Mrs Charles said she had received no information on the meeting and criticised the Government’s response to Harry’s case as “very poor”.
She added: “We’re UK citizens, we should be the ones that are being protected, we should be the ones that they are fighting for.
“Although they keep saying that they’re clearing the path for justice, tell us what they are doing then, communicate with us.
“Until they do, we’re going to continue to be suspicious that something else is going on behind the scenes, so I would just ask them to come and talk to us.”
Mr Trump was asked about the case by reporters in London ahead of meeting Mr Johnson.
He repeated the US position that Mrs Sacoolas had diplomatic immunity but said he had also met her, adding: “We’re trying to work something out.”
It is understood that Harry’s parents have also expressed their “misery” to the Crown Prosecution Service over the time it has taken in deciding whether or not to charge Mrs Sacoolas.
Harry, 19, was killed outside US air base RAF Croughton in Northamptonshire on August 27.
Mrs Sacoolas initially co-operated with police, but then claimed diplomatic immunity and fled to Washington DC and has refused to return.