Unite union members at Carlton walked out for 48 hours earlier this week and are set to man the picket line next Monday and Tuesday. The union said 54 workers were excluded from a pay rise that the company's 800 staff were given in 2009.
However, Premier Foods said Unite workers at other Premier Foods factories had accepted a similar deal and that bakers at Barnsley were crossing the picket line to get to work.
A spokesman added: "We are really disappointed at the action of 35 engineers, which undermines the future of the factory and that of our 800 permanent employees. The offer they have rejected mirrors the offers accepted by the Unite union at many other Premier Foods sites and will not be improved."
Union representative Pat Pepper said that because there was no offer on the table, members planned to continue striking until there was some serious attempt at negotiation.