Liberal Democrat Icknield councillor Jeff Petts would like to see people charged £10 when they miss an appointment, he told the borough council's scrutiny health and social care review group on January 13.
Referring to a local surgery where "cancellations and no shows remaining stubbornly high at 140 a month", he asked: "Is there any work being done on that?"
Director of primary care at the BLMK Clinical Commissioning Group Nicky Poulain replied: "That's an internal problem for practice management. If you want to cancel your appointment we need to make it easy.
"If you can't get through to the practice to cancel it, you're not going to. For those patients that don't, the GPs write to them once they've done it twice.
"If you've any ideas we'd welcome them because it's a waste of resources."
Councillor Petts suggested "taking their credit card number and charging them £10 every time they miss one", but both he and Ms Poulain accepted "that's not going to happen".
She added: "I don't think people realise that it denies someone else a booked appointment.
"It may be the difference between someone inappropriately going to the accident and emergency department because you don't need an appointment there."
Labour South councillor David Agbley warned: "There's no way we should be charging for missing appointments because there are so many reasons why residents don't turn up.
"We need to educate people to understand the effect on GPs and surgery staff if they're not going to attend, and that they need to cancel it to make sure the appointment is open to others."
Labour Northwell councillor Anne Donelon said: "I do understand councillor Petts' frustration. But we can't be charging people.
"We can't have people paying when we look at the NHS, even if they miss their appointments."
Ms Poulain explained: "We've 26 practices working across five primary care networks. In any month, there are 96,000 appointments.
"We've about a 220,000 population registered with GP surgeries in Luton. And to do some myth-busting 70 per cent of those were face-to-face.
"Primary care is a 365-day service, 24/7. We need to get that offer correct in Luton. We don't want people rocking up to the accident and emergency department. That's our aspiration.
"Any person who is able to walk into accident and emergency is triaged and channelled over to a GP primary care service. We're encouraging our residents to register with a GP practice and there shouldn't be any barriers.
"There's support to practices for telephony because we realise if you ring and you don't know where you are (in the queue) it's quite frustrating. We encourage patients not to all do it at 9am because we get peaks and troughs."
There were 1,200 calls across Bedfordshire to the 111 service, almost double the usual amount, on the recent bank holiday weekend.
"The numbers accessing the service was huge," she said. "Hence answering the telephone within one minute was appalling. We went as low as ten per cent. But it took about 90 seconds.
"Although they didn't meet the target of 60 seconds, I appreciate that one-and-a-half minutes is a long time when you're on the end of a phone and wanting urgent primary care access."