"The meeting was extremely positive. He is wholly supportive of the Gurkha cause. He is going to come up with a new solution by the end of this month," Ms Lumley said.
She added: "I trust him. I rely on him. And I know that he has now taken this matter into his own hands and so today is a very good day."
Ms Lumley said she accepted the Prime Minister would have to deal with the issue "slowly and deliberately" but added his commitment to bring forward the processing of all outstanding applications from July to May had already shown "a huge intent and purpose".
She said: "He promised he would do all he can ... I do trust the Prime Minister. I know him very slightly personally and I find him to be a man of integrity.
"I think this is now in his hands. It has been in many people's hands. It has been bandied around from the Ministry of Defence to the Home Office and all kinds of different people have been dealing with it.
"Now, I feel we have got the head man, the man at the top, the leader of our entire nation and I feel absolutely confident he is going to do the right think for the Gurkhas."
Ms Lumley said some "wild figures" had been bandied around about the cost of allowing the Gurkhas to settle in the UK - which the PM last week put at £1.4 billion.
But she said she and Mr Brown did not go into the detail of the cost during their meeting.
And she added: "I hope we can all look at this with a steady head and realise that this is utterly achievable, utterly attainable."
Downing Street said it had been a "positive" meeting.
"It was a friendly meeting, it was a constructive meeting," the Prime Minister's spokesman said.
"The Prime Minister listened to Miss Lumley's concerns and proposals and made clear his admiration and gratitude for the Gurkhas' contribution over the years."
The spokesman added that Mr Brown had said he would want to look at Miss Lumley' proposals in the next stage of the Government's consideration of the issue.
Under rules set out last month, Gurkhas who retired before 1997, when their base moved from Hong Kong to Farnborough, Kent, have to meet certain criteria to settle in the UK.
Medal winners, officers and injured soldiers are included but thousands of ordinary riflemen are not.
Ministers were required to look again at their guidance for pre-1997 Gurkhas after the High Court ruled it was unclear.
Last week Mr Brown suffered a humiliating Commons defeat when 27 Labour rebels helped vote through a Liberal Democrat motion calling for all former Gurkhas to be allowed to settle here.
Asked at Prime Minister's Questions this afternoon whether he felt the Government was "bound" by that vote, Mr Brown said simply that it would "listen to the voice of the House as it was expressed last Wednesday.
"We are speeding up the 1,500 applications and hope to have them completed by the end of May. We are looking at the judicial reviews as a matter of urgency and will complete this work very soon," he told former Tory leader Iain Duncan Smith.
"We will come back to the House with a statement. I have always said we wanted to do this stage by stage."
Speaking after the PM's meeting with Ms Lumley, Mr Duncan Smith told BBC News: "I asked the Prime Minister today a very straightforward question...he was all over the place and I understand he's not given an absolute answer to Joanna Lumley.
"I'm not in a position of trusting anybody any more in this game because they have been spun from start to finish.
"The answer is very simple: at some stage the Government is going to have to say 'we accept the will of the House and now we will simply make the legislation and do all the relevant things that allow the Gurkhas to settle here'."
Keith Vaz, who chairs the Home Affairs Select Committee which has called for universal settlement rights for Gurkhas and who was among the Labour rebels, welcomed today's talks.
But he also blamed Cabinet in-fighting between Home Secretary Jacqui Smith and Defence Secretary John Hutton for the humiliating Commons defeat.
"I am very pleased that the Prime Minister met with Joanna Lumley today," he said.
"The Home Affairs Committee has accepted the invitation of the Immigration Minister to host a seminar on finding a way forward to resolve the Gurkha issue. The seminar will be held as soon as possible."
In a separate article for Progress magazine about the lost vote, he said: "I felt that the whole issue was mishandled. Whatever in-fighting occurred between the Home Office and the Ministry of Defence caused chaos which resulted in the Government being defeated."
Following an inquiry last year, Mr Vaz's committee called on the Home Office and MoD last November to take urgent action to extend settlement rights to all Gurkhas. But he said it was six months before the Home Office responded by setting out new guidelines - only for Ms Smith to then email Labour MPs during last week's debate to set out a further change in policy.
"That is not the best way to handle a sensitive policy of this kind," said Mr Vaz.
Ms Lumley refused to be drawn on which senior Royal has sent her a letter indicating their support for her campaign.
"I will never tell any of you. I have actually never told anybody who it is and I won't," she said.
When asked if it was the Prince of Wales, who is colonel-in-chief of the Royal Gurkha Rifles, she replied: "No it wasn't."
The actress told the Home Affairs Committee yesterday that she had written to Mr Brown to request a meeting three times but had received only one reply from an aide.
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