As many as two million people have to wait up to three weeks for an appointment with a GP, a survey has found.

Half a million face a wait of up to a month to see their family doctor, while only one in three patients is able to secure a same-day appointment.

The research, carried out by the Daily Mail and over-50s group Saga, found that 20% of people cannot get a consultation within seven days.

Last week the Royal College of General Practitioners (RCGP) claimed more than 34 million people will this year fail to get an appointment with their GP when they seek one.

The RCGP prediction, based on the GP Patient Survey, published in December, suggested the number of people failing to see their doctor when they want will rise as government cuts and the effects of an ageing population take hold.

Leading doctors have blamed the struggle on the decline in funding for healthcare in the community and an increase in patient numbers.

Dr Maureen Baker, chairwoman of the RCGP, told the newspaper: "We do worry on patient safety grounds that access is becoming more of a problem.

"Take someone who's had a cough for four or five weeks. The chances are that it's a long-running cough from a viral illness. But what if they've got TB, what if they've got lung cancer?

"It if does turn out to be cancer or TB then the quicker they're dealt with the better."

The Mail's survey questioned 11,019 adults online over a 10-day period last month and asked them how long they waited the last time they saw a family doctor.

More than one in five, 22%, said they waited longer than a week, and 4% waited two to three weeks.

A further 1% waited longer than three weeks and a "handful" waited for more than a month. Nationally, 4% equates to two million people, and 1% to 500,000.

The survey also found that patients felt it harder to book appointments now than five years ago. Some 49% said it was "difficult or very difficult" compared with 21% in November 2008.

GPs now see 340 million patients per year, but the NHS budget for general practice has been cut by £9.1 billion in real terms since 2004, the RCGP said.

Each GP is handling 1,500 more consultations a year than in 2008.

Saga Health Insurance has introduced a 24-hour GP helpline that enables customers to speak, in confidence, with a qualified, practising GP at a convenient time about any medical concerns.

The over-50s are able to discuss any symptoms they might have, treatment options, side effects of medication and even after-effects of surgical procedures. Customers can also receive advice about vaccinations if they are planning to travel abroad.

Roger Ramsden, chief executive, Saga Services, said: "With the nation's over-50s leading busier lives, with many working well into old age, it is important that the health service adapts and doctors work seven days a week. This survey amongst our customers shows that more needs to be done to serve the needs of this age group who are the biggest users of GP services.

"We've recognised that people are finding it hard to speak to their doctors, which is why we've introduced a 24-hour GP telephone consultation service for all our health insurance customers."

A Department of Health spokesman said: "This is based on misleading extrapolations of partial data. The most recent GP survey, a comprehensive exercise responded to by nearly one million people, showed the vast majority of patients are satisfied with their GP and rated their experience of making an appointment as good.

"But we want to do even more, and our changes to the GP contract, including a specific named GP for all over-75s, mean the return of proper family doctors and a more personalised service for patients."