The Social Market Foundation said forcing people to pay a fee for an appointment could help the NHS cope in the tight financial times ahead.
The group said it would not breach the values of the NHS as charges already applied to dentistry and prescriptions
But both the government and doctors said they were against such a move.
The think-tank said the NHS was facing a tough couple of years.
“ All patients have a right to free healthcare that is based on their clinical needs, not the size of their bank balance ”
Dr Chaand Nagpaul, of the British Medical Association
While funding is guaranteed until 2011, many are expecting the budget to be frozen or cut after that.
The Social Market Foundation said the only way for the NHS to cope was to raise taxes to put more money into the system, limit demand or work more effectively.
The NHS is already looking to make savings and the think-tank said there was little appetite for tax rises.
Instead, they said charging for GPs would be a good way to reduce demand.
Report author David Furness said: "It would get people thinking twice about whether the visit was essential.
"If we don't introduce rationing like this, there will be rationing by stealth through waiting lists, crumbling hospitals and poor quality services."
Opposition
He said the move was not about making money and insisted even a small charge like this could help reduce appointments by about 5%.
He said children and those receiving tax credits should not be charged and said the think-tank was opposed to fees being levied on any form of emergency care.
But Dr Chaand Nagpaul, of the British Medical Association's GPs committee, said the union was opposed to charging.
"All patients have a right to free healthcare that is based on their clinical needs, not the size of their bank balance.
"I would also be concerned that charging some of my patients to see me would undermine the doctor-patient relationship. Many would be put off coming to their local surgery when they might need care."
A spokeswoman for the Department of Health said ministers were also against introducing charging like this.
She said it would be against the "founding principles of the NHS".
