The Prime Minister said she hopes a presumed consent organ donation system will "give the gift of life" to more people, as she met transplant patients.
Theresa May and Health Secretary Jeremy Hunt visited the Royal Liverpool University Hospital, following her announcement last week of the move to an opt-out donation system.
They met kidney transplant patients including Holly Shaw, 30, who had a second kidney transplant last year.
Ms Shaw told the Prime Minister she had waited for three and a half years for her first transplant in 2008.
She said: "It was just awful, basically, just hanging on waiting for that phone call."
In 2016 she had a second transplant after her mother donated a kidney.
Speaking after the meeting, Mrs May said: "It's great to be here at the Royal Liverpool and actually meet people who have benefited from kidney transplants and what they have told me about is how that has actually transformed their lives and therefore how important it is for people to be willing to donate organs and that is what the opt-out scheme is about.
"It's about saying that in future, rather than having to opt in to give consent that when you die your organs can be donated to somebody and give somebody the gift of life, that actually the presumption will be that your organs will be available and if you don't want that you have to opt out.
"What this will do, I hope, is mean that more organs will be available for donation, more people will be given the gift of life and see their lives transformed."