Gordon Brown says Britain should consider an "opt-out" system of consent for organ donation.
The prime minister's call for hospitals to be allowed to remove organs from dead patients without prior consent comes before a government taskforce reports on the issue next week.
Mr Brown, writing in the Sunday Telegraph, says he wants to "start a debate" about whether Britain should consider raising its organ pool from the 25 per cent of Britons currently registered.
Two-thirds of Britons are positive about organ donation but are not positively registered donors, he writes, suggesting an "opt-out" system may be more effective to raise the actual donor levels above the current 13 per million in the UK population.
"We may need to do more to encourage more of us to donate," he writes.
"A different consent system, more like the one used in Spain, could serve to increase donation levels significantly.
"Of course, any 'opt-out' system would - in cases where the potential donor is not on the register - leave the final decision with the family: that is only right and proper.
"But a system of this kind seems to have the potential to close the aching gap between the potential benefits of transplant surgery and the limits imposed by our current system of consent.
"A serious debate - involving the public most of all, but also bringing in professional views and those of religious leaders - is long overdue."
There are currently around 13 million people on the NHS organ donation register but because not all organs are suitable for transfer Britain suffers a demand shortfall.
Only around 3,000 transplants take place each year despite 8,000 people needing a new organ.
As a result one person per day is dying on the transplant waiting list as a result, something Mr Brown describes as an "avoidable human tragedy we can and must address".