LMCs report practices being inundated with requests, with GPs in some parts of the country facing daily requests for help with claims.
Glasgow LMC medical secretary Dr John Ip said local GPs were being asked by one or two patients a day to provide letters in support of appeals.
Changes to housing benefit and disability living allowance have been highlighted as key factors behind the workload rise for GPs.
LMCs, including those in Glasgow and Birmingham, have produced posters and sent out letters urging patients not to ask GPs to support their appeal.
The poster produced by Birmingham LMC reads: 'GPs provide medical care to their patients and are not in a position to administer nor to police the benefits system. It is not appropriate for the GP to be asked for letters of support or letters to confirm housing or care needs.'
GPC deputy chairman Dr Richard Vautrey said the government needs to invest 'properly' in independent occupational health assessments as part of the benefit changes.
He said: 'GPs are seeing an increase in patients asking for letters to support a variety of benefit appeals. This is an unnecessary additional workload on already overstretched practices and GPs shouldn't have to pick up the pieces created by the government's failure to invest properly in independent health assessments as part of the benefit changes.'
Asked about workload implications, he said: 'It isn't just the appointment. It is also the time needed to produce the letter afterwards, which includes reviewing records.'
Dr Vautrey said it was up to individual practices if they refused to provide support, but they needed to have a 'consistent approach' for all patients. 'Practices are within their rights to charge a fee but these are people who are least likely to be able to afford such a payment,' he added.
Dr Ip said: 'This is having the effect of increasing GP workload considerably. This is wholly inappropriate and it takes appointments and GP time away from frontline clinical care.'
A Department for Work and Pensions spokesman declined to comment.