Plant, which is in administration and has been operating at about half capacity, stopped product deliveries on Tuesday
The Swiss refiner Petroplus's British Coryton refinery is expected to resume oil product deliveries in 24 to 48 hours, a union official has said.
Petroplus is filing for insolvency, putting over 2,000 jobs and the operations of five refineries across Europe at risk after it defaulted on $1.75bn (£1.1bn) of debt.
The Coryton refinery, which can process 175,000 barrels of crude oil per day, is under UK administration. The plant has been operating at about half capacity, but stopped product deliveries on Tuesday, leading to fears of petrol supply shortages in the south-east.
"I spoke to the senior management about an hour ago and, because they are in administration rather than liquidation, they are legally able to trade, but it is at the discretion of the administrators," Russ Ball, the regional industrial organiser for the Unite union, said.
"They are looking to resume supplies in the near future – hopefully within 48 hours."