Members of the Rail, Maritime and Transport union employed by contractors Servest UK walked out at 06:00 GMT.
The RMT union is calling for agency workers to be made members of GWR staff to end the current situation of a "two tier" workforce.
GWR said it is aware of the action by one of its contractors but added it would not impact on rail services.
The dispute, involving almost 200 workers, is over a number of issues including pay, annual leave and the use of agency workers.
Mick Cash, RMT general secretary, said affected members had voted "decisively" for action.
"GWR and Servest UK need to do the right thing and immediately resolve the issues relating from the transfer of staff and bring these workers back in house so that they are on the same terms and conditions as the rest of the staff."
A second 24-hour strike by the RMT is planned for 23 December.
Cleaners on the Great Western Railway have gone on strike in a dispute over pay and conditions.