Two services providing out-of-hours medical care are missing key targets in the time taken to deal with calls.
Latest results show that NHS 111, run by Derbyshire Health United, has missed targets for calls answered within 60 seconds and calls returned with 10 minutes.
The out-of-hours service, run by Central Nottinghamshire Clinical Services (CNCS), missed three targets.
It is expected to assess 95 per cent of the most urgent calls in 10 minutes, others in an hour and begin home visits within two hours.
Instead, the figures were 88 per cent, 85 per cent and 84 per cent respectively.
A member of CNCS staff, who asked not to be named, was so concerned he contacted the Leicester Mercury.
He said: "There was one Saturday evening recently when there was just one GP on duty for four hours.
"There should have been at least three of them but CNCS can't recruit them to cover all the shifts.
"There were so many calls waiting for assessment and patients were irate.
"A number of us are really worried someone is going to die and it could be your mother or father."
He said officials from East Leicestershire and Rutland clinical commissioning group (CCG) – which is responsible for the contract – carried out a spot-check the day after he contacted the Mercury. He said: "I was told that GPs were offered enhanced rates to cover the shifts that evening."
Deputy city mayor Councillor Rory Palmer, who is also chairman of the city's health and wellbeing board, said: "I want clear reassurance there is adequate out-of-hours cover, that people are getting the right advice and support and there is an adequate team of medics.
"There seems to be an issue about how joined up and coherent these services are."
When GP surgeries are shut, patients have to call 111 and then, if necessary, the call is referred to the out-of-hours services where calls are assessed by a GP.
Robin Wintle, associate director for contracts at East Leicestershire and Rutland CCG, said: "Patient safety is of paramount importance and we take any situation which could affect the quality of care patients receive very seriously.
"We are aware there have been issues with staffing levels and we are monitoring the situation weekly, in line with the requirements of the contract.
"We are aware CNCS has flexible contingency arrangements that have ensured disruption to services is minimised when appropriate clinical rotas are not in place."
Mr Wintle said a spot check on Tuesday did not reveal any quality or safety risks.
Stephanie Goodall, director of services at CNCS said: "We have reviewed a number of operational areas, as part of a recent organisational wide restructure.
"Following completion of the staff consultation, there have been changes which will address concerns with staffing levels."
Dr Saurabh Johri, clinical lead for the 111 services, said he expected all targets to be met by September 9, the anniversary of the start of the contract.
Latest figures show 88.8 per cent of calls to 111 were answered within a minute, against the required 95 per cent.
