Bereaved families have blocked the donation of organs from 547 UK registered donors since 2010 - about one in seven cases, figures show.
NHS Blood and Transplant (NHSBT) says it will no longer seek the consent of families formally, to make such "overrides" more exceptional.
Instead, they will be given a leaflet explaining consent - or authorisation in Scotland - rests with the deceased.
Families can still veto that consent but must provide reasons in writing.
NHSBT expects the change to lead to a 9% rise in donors.
It said the 547 blocked donors would have provided organs for 1,200 patients.
There are currently 6,578 people waiting for transplants in the UK.
Last month, the system in Wales changed to "presumed consent", under which people are deemed to be potential donors unless they have specifically opted out.
NHSBT head Sally Johnson, said: "We are taking a tougher approach - but also a more honest approach.
"My nurses are speaking for the person who has died. People who join the register want and expect to become organ donors.
"We do not want to let them down."
She added: "We have every sympathy for families - and of course we do not want to make their grief worse.
"We think this will make what is a hugely distressing day easier for them, by reducing the burden on them.
"The principle that the individual affected is the one who consents applies throughout medicine, and it is not different because someone has died."
Specialist nurse James Hardie, from St Mary's Hospital in London, said: "Families sometimes override their relative's wishes because they perhaps did not know that person was on the register.
"They find it distressing that they did not know their loved one as well as they thought."
But he added: "The consequence of refusal is that people die as a result - that is the unfortunate reality of the situation.
"If somebody refuses the opportunity for their loved one to become an organ donor, somebody potentially goes without a transplant."
The British Medical Association said families should be strongly encouraged to respect the views of the deceased.
But it said that in the small number of cases where they had such strong and sustained opposition it was likely to cause them severe distress, donation might be inappropriate.