In April last year, the government began to reassess 1.5m people across the UK receiving incapacity benefit.
Claimants have undergone 'work capability assessments' to determine whether they are fit for work. But GPs say many patients deemed fit visit them to seek help to overturn the ruling.
GPC deputy chairman Dr Richard Vautrey said: 'The new assessment means that a lot of patients are not achieving the necessary points required. This leads to a large number of them coming to their GP seeking support for an appeal.'
Dr Vautrey said that, in the past two weeks, he had personally seen five patients and dealt with requests from agencies about two more regarding appeals.
GPC Wales chairman Dr David Bailey estimated that his practice saw 10 patients a week seeking help with an appeal.
'This is happening all over the country; it's a UK government policy,' he said.
Dr Vautrey said GPs were left in a difficult position by patients asking for help because the work was unfunded.
'The GP could potentially charge the patient or they could charge other organisations asking for support,' he said.
'GPs are left in a very difficult position because by the very nature of the patients being on benefits, they cannot afford to pay.'
GPC contracts and regulation subcommittee chairman Dr John Canning said it was fine for GPs to charge for the work, as it was done within their own time, and often required the input of other practice staff.
'Charges discourage frivolous requests. If you don't ask for payment, people start asking for more and more,' he added.
A Department for Work and Pensions spokesman said: 'If someone disagrees with the outcome of their work capability assessment, they have the right to appeal.'