A survey shows how patients have to wait for GPs, like this one, wearing a badge supporting the junior doctors' strikeReuters

Over 10 million patients a year are struggling to get an appointment with their GP with more people than ever unhappy at restrictive opening times, a comprehensive NHS study has found.

The proportion of people who are unhappy with the opening times of their local practice has risen by one fifth in three years, with many pleading for a seven-day a week service.

The study showed how some practices would be closed for up to three and a half hours at lunchtime or sometimes even closing their doors one afternoon a week.

The Department of Health's GP Patient Survey – a snapshot of 854,000 adults – shows 18% say their practice opening hours are inconvenient. It shows the numbers waiting at least a week to see a GP rose to 10.2 million nationally, up from 8.5 million in 2012.

Katherine Murphy, chief executive of the Patients Association, said: "We know many surgeries are struggling to cope with demand due to a lack of funding, and a shortage of staff. There must be further investment."

Maureen Baker, Chairman of the Royal College of GPs, said family doctors were working harder than ever to meet increasing demand from a growing and ageing population, but did not have enough resources to do so.

She said: "Our service now receives just over 8% of the overall health service budget – despite making 90% of all NHS patient contacts, and our work becoming greater in both volume and complexity. This is not safe for us, and it is not safe for our patients," the Daily Telegraph reported.

Patients' groups said an increasing reliance on female GPs, often working limited hours, meant some surgeries were offering an increasingly "part-time service".

Joyce Robin, from Patient Concern, said the situation had become "hopeless", telling the Telegraph: "The situation has become ridiculous – it is dire. When you have got surgeries closed for these sorts of periods, you haven't really got a GP service in place, it's just a part-time operation."