Max's Law - named after Max Johnson, 10, who was saved by a heart transplant - was backed by ministers in Parliament.
The proposal is set for further scrutiny in Parliament, but would see 'presumed consent' introduced in England following the move to an opt-out system in Wales.
It comes two years after The Gazette in Blackpool and the Lancashire Post in Preston launched the 'Lancashire: Giving the gift of life' campaign urging more people to become donors.
Health minister Jackie Doyle-Price said: "We are determined to ensure we secure more organs available for transplant, because we are very concerned we are losing lives unnecessarily.
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"At this stage it's rather too early to draw any conclusions about the number of organs the change in Wales has secured, but we have seen an increase in consent and opting onto the register.
"Our best estimates are that this change will secure an additional 100 donors a year, which could lead to the saving of 200 extra lives.
"On the basis that we could save 200 lives, we will wholeheartedly support this bill."
Labour leader Jeremy Corbyn urged MPs to back the plans, while health secretary Jeremy Hunt was on the government's front bench to hear Ms Doyle-Price's comments.
At the Tory party's conference last year, Prime Minister Theresa May indicated the government would look to move to an opt-out system.
MPs heard that around 1,000 people die every year while waiting for a transplant and England had some of the lowest rates of consent for organ donation in western Europe.
And across Lancashire, 134 people have died while on the waiting list in the past decade, with 133 were still in need of a life-saving transplant.
“It’s a tragedy that people are dying unnecessarily every year in Lancashire waiting for transplants,” assistant director of organ donation and transportation for the NHS, Anthony Clarkson said previously.