The British Medical Association (BMA) meeting in Cardiff heard that a system of "presumed consent" - where people would opt out of donation rather than opting in - would help boost donor numbers.
Doctors at the conference rejected calls for them to reconsider their stance in favour of presumed consent amid claims it could erode patient trust in donation.
No part of the UK has introduced a system of presumed consent so far, although Wales has said it intends to do so.
Dr Evan Harris, the doctor who first proposed the motion setting the BMA's policy on presumed consent in 1999, said a system of presumed consent was better for patients, doctors and relatives of the donor.
"The vast majority of people would wish to help save lives after their death, but the problem is the current system sees nearly half of relatives withholding their permission because they are uncertain (of what to do]," he added.
"The evidence is very good that presumed consent is effective and acceptable in countries where it has been introduced."
Meanwhile, a bid to reduce the legal abortion limit from 24 to 20 weeks of pregnancy was rejected by delegates.