The food outlet said it was seeing “temporary interruptions” to some products containing chicken – although its popular chicken bake is still available.

The problems at Greggs come just days after MacDonald’s admitted it had run out of milkshakes and bottled drinks. Last week Nando’s was forced to temporarily close 50 of its 400 UK restaurants due to supply chain issues, and sent staff to help out at the chain’s suppliers.

Meanwhile, Sainsbury’s stores in London and the South East could face empty shelves after DHL lorry drivers at the supermarket’s Dartford distribution centre signalled their willingness to strike over pay.

DHL is contracted to run Sainsbury’s Dartford regional distribution centre, including driving and warehouse operations. Union Unite has held a consultative strike action ballot of HGV drivers employed by DHL at the Dartford distribution centre over a 1% pay offer put forward by the logistics company.

The ballot of about 200 Unite HGV driver members resulted in a 98% vote in favour of taking industrial action, including strikes.

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Unite regional officer Phil Silkstone said: “Unless Sainsbury’s and DHL, both of which run extremely healthy profit margins, get their acts together there will be empty shelves in Sainsbury’s stores across London and the south east of England.

Seema Malhotra, Labour’s shadow minister for business and consumers, said: “The chaos hitting supply chains is of the Conservatives’ making. Their failure to keep their promise to cut red tape for businesses, which are struggling with more paperwork and higher costs, combined with worker shortages, has created a perfect storm.

“Whether it’s production grinding to a halt in our car factories, shelves emptying in supermarkets, or restaurants running out of food and drink, businesses are ringing the alarm and saying these problems are only going to get worse.

“Ministers must listen to businesses and unions who are calling for them to show leadership and put in place short-term solutions to deal with this acute crisis. But they must also end their chronic dismissal of these concerns, having accused the industry of ‘crying wolf’ over driver shortages, and take action to deliver on the promise of post-Brexit Britain.”