Gordon Brown has admitted the NHS needs to improve night and weekend GP cover after the system was criticised by an inquiry into the death of a woman.
Ms Campbell consulted eight Camidoc GPs
A report into the death of journalist Penny Campbell who consulted eight doctors over Easter in 2005 said there was confusion over the system.
GPs were allowed to opt out of the responsibility in 2004, leaving it to private firms and groups of doctors.
The inquiry said the system was seen as a holding bay until full cover resumed.
The chancellor, soon to take over as prime minister, said: "The health service has got to be there for people when they need it and we need to do better in the future.
"What I've been talking about is how we can extend the range of facilities for health care at weekends and out of hours.
"We need more access to doctors, we need drop-in centres, we need local health care centres to be more effective, we need NHS Direct to be working."
Ms Campbell, a 41-year-old mother-of-one from north London, died two years ago after developing septicaemia following routine surgery.
She spoke to eight doctors working for Camidoc, the local GP out-of-hours service, over the four-day break.
None of the doctors identified the septicaemia and this lack of diagnosis contributed to her death, an inquest said last year.
The inquiry said a major systems failure by Camidoc - over passing on information - meant each call was treated as an individual episode.
And it added Camidoc's roots as a small co-operative meant that it was not fully prepared for its rapid transformation into a major provider of out-of-hours care.
The report said Camidoc should improve its governance and the four PCTs which pay for the service - Camden, City and Hackney, Haringey and Islington - should develop action plans to address the failings identified.
Camidoc and the PCTs have apologised and promised to take action.
Dr Ivor Robinson, from Camidoc, said: "We are trying to learn the lessons... but to dismiss a whole service with a 10-year record is unfair."
'Learn from lessons'
It also called on the doctors involved - two of which are now subject to further investigations by NHS managers - to reflect on the case.
But the report said the failings should also be seen in the context of the changes to the GP contract in 2004 which allowed doctors to opt out of weekend and night care.
In total, nine in 10 GPs opted out of the responsibility.
A variety of arrangements are being used across England to provide out-of-hours cover, but the most common is a co-operative, like Camidoc, which are not-for-profit organisations set up by GPs to cover regions.
Gordon Brown has said the NHS must do better
The inquiry said the perception of out-of-hours care as a "holding bay" until full GP care resumed needed to be addressed.
And it warned there was "policy confusion" over whether an out-of-hours service was for urgent or unscheduled care.
Ms Campbell's partner, Angus MacKinnon, said a return to the old arrangements where GPs had responsibility would be "better than the existing system".
Dr Michael Dixon, a GP and chairman of the NHS Alliance, which represents PCTs, said: "The old system was not perfect. You had GPs who were too tired to provide a proper day-time service.
"But I think there are lessons that could be learned."
The Department of Health has said the case was not about the changes introduced.
But it has asked for PCTs to review their arrangements in light of the case.
Lib Dem health spokesman Norman Lamb said addressing concerns about out-of-hours care should be a priority when Mr Brown becomes prime minister.