In these circumstances, it makes sense to opt for whoever can see you first. Most patients - with the important exception of the chronically ill, who make regular visits to the surgery - want rapid treatment and are less concerned about who provides it. But that means that the link with the personal family doctor is weakened.
In a society in which round-the-clock shopping, banking and TV are taken for granted, medical advice remains astonishingly hard to obtain. GPs' surgeries are open for a couple of hours morning and evening, and if you cannot get an early appointment the only alternative is to queue for a couple of hours in the walk-in surgery.
As the Prime Minister noted in a speech to GPs earlier this month, although most patients are happy with the care they get, they are less happy with how long they have to wait for it.
That is about to change. The scale of the change that is planned has been unheralded and little written about. Put simply, it is to replace GPs with nurses as the first point of contact for patients. This change will fundamentally alter the way patients obtain medical treatment, by opening up a new gateway to the NHS. It could even spell the end of the traditional GP.
Major changes in social institutions are always difficult to date. But the winter crisis in the NHS last Christmas may have set the seal on a process whose origins can be traced back years or even decades.
There were four days over the holiday when hospital casualty departments were overwhelmed with patients suffering from flu. Beds were full, trolleys were wheeled out and the health service found itself unable to cope.
Nothing new there, of course. But when the causes of the winter crisis were investigated, it was GPs who got the blame. Because Christmas fell at a weekend, surgeries were closed for longer than normal. Out-of-hours deputising services were unable to cope and scores of sick patients took themselves off to their local accident and emergency departments.
What ministers saw as the failure of the primary care service over Christmas chimed with government plans for its reform. The Christmas crisis helped forge Tony Blair's speech in Birmingham earlier this month to a conference of GPs, nurses and managers in which he set out his vision of the NHS in the 21st century. A key aspect of that vision is instant access to medical advice when people need it.
Ministers are determined to do something about the problem of access, a key determinant of the way people perceive the NHS. Nurses, who would be contacted by telephone or via the Internet, would provide a filtering system, helping patients with minor ailments to treat themselves while referring trickier cases to... how shall we describe this new style of second- line general practitioner? Not so much a family doctor, seeing everything that comes through the door of the surgery; more a "primary care consultant", perhaps.
Here we have the medical equivalent of 24-hour banking, an image used by Tony Blair last week. For everyday problems, patients would be able to seek instant advice, 24 hours a day, from the nurse-run telephone helpline, NHS Direct, which is being rapidly rolled out across the country. Access points are to be established in post offices and libraries. Computer links (the medical cash machine) and a network of walk-in centres led by nurses would provide hands-on care. Doctors, like bank managers, would offer appointments for more serious problems.
It is, of course, far too early to tell how far this process will go. Much will depend on the response of the public and of the professional groups. But the direction of travel is clear. Stephen Thornton, director of the NHS Confederation, said the vision set out by the Prime Minister in Birmingham last week required "nothing short of a complete transformation".
It has, however, an undeniable logic to it. For more than two decades, health policy makers have worried about using expensively trained doctors to hand out cough medicine and laxatives to the worried well. Surveys show that GPs consider many of the problems brought to them are trivial.
In the Seventies, there was talk of introducing Third-World-style barefoot doctors to the UK - medical orderlies who would sort the simple problems from the serious. What curbed these moves were warnings from the royal medical colleges that an apparently trivial symptom could hide a serious underlying disease. Only a trained doctor, taking a full history and making a proper investigation, could tell the difference. For patients to place their health in the hands of nurses risked disaster.
That view is now history. What has made the use of nurses possible as front-line practitioners is the development of computer-based protocols - lists of questions that cover all eventualities. The protocols used by NHS Direct have been adapted from America and so far the service has met with almost universal approval.
Surveys of callers in the three pilot sites have shown 97 per cent satisfaction with the advice received - even though it came only from a nurse. In some cases lives have been saved, but more often patients who would otherwise have turned up at the surgery or accident and emergency department have been helped to deal with the problem at home, saving themselves the trip and the NHS a consultation.
Nurses are understandably enthusiastic, but GPs notably less so. They feel their territory invaded and their autonomy threatened. The BMA warns of threats to continuity of care and the doctor-patient relationship. It knows that if the role of GPs providing round-the-clock care to a defined list of patients is eroded, they could lose their coveted status as self- employed, independent contractors with the NHS.
But GPs have been living on borrowed time since 1995, when they negotiated an end to their contractual requirement to work at least some nights and weekends. Although they remain technically responsible for their patients 24 hours a day, in practice many work something close to normal office hours.
Now they are being reorganised into "primary care groups" comprising GPs, nurses, health visitors and other staff, which will ultimately control more than three-quarters of the NHS budget. These groups will serve populations of an average of 100,000, providing their primary care and buying their hospital care within a fixed budget - the first time GPs have been cash- limited in this way. They will therefore have a financial incentive to encourage any innovation - such as the greater use of nurse-led advice and care - that improves their efficiency.
The strategy is, however, not without risk, as Professor Chris Ham, a health policy expert at the University of Birmingham, has warned. Britain has a unique system of general practice that provides care to the entire population and is admired across the world. Its strength lies in the personal relationship between patient and doctor. For many patients, who need only occasional attention, continuity of care by a familiar doctor may not matter. But for those with chronic conditions, who tend to be older, it matters more.
Bringing nurses into the medical front line is overdue and could yield real benefits for patients in terms of convenience and speed of access. But if the personal link between patient and doctor is broken, a pillar of the NHS will be lost. This will depend on whether the new nurse-led advice system is to be an additional service or merely a money-saving replacement for the traditional GP.