Two more people have died after eating pre-packaged sandwiches and salads linked to a listeria outbreak, taking the total number of deaths to five, Public Health England has said.

The health secretary, Matt Hancock, ordered a review of hospital food on Friday as he came under pressure from opposition MPs, who demanded that he make a statement to parliament on the scandal.

“I have been incredibly concerned by this issue and strongly believe that we need a radical new approach to the food that is served in our NHS,” Hancock said. “Staff, patients and families deserve so much better – our NHS should be at the forefront of supporting people to make healthy choices. I have instructed the NHS to conduct a root and branch review of hospital food.”

The source of the infection is understood to relate to products supplied by the Good Food Chain and the affected sandwiches and salads have since been withdrawn from hospitals.

PHE said evidence suggested all those who died ate the products before the withdrawal took place on 25 May.

The investigations into the outbreak continue and were being conducted in partnership with the Food Standards Agency (FSA), it added.

The first three deaths were at Manchester University NHS foundation trust and Aintree University Hospital NHS foundation trust in Liverpool.

It is understood that of the latest two deaths, one died after the first three confirmed cases. The other died before the other three, but has only just been discovered to be linked.

The trusts where the latest two deaths happened have not yet been named, but PHE said there were seven trusts across the country dealing with listeria cases.

The first case showed symptoms on 25 April and sandwiches and salads were withdrawn on 25 May, as soon as a link with the cases was suspected.

It is understood that some of the products were sold at hospitals while others were given to patients.

The Good Food Chain, which supplied 43 NHS trusts across the UK, has voluntarily ceased production. The business was supplied with meat from North Country Cooked Meats, which has since tested positive for the outbreak strain of listeria and also stopped production.

Hancock was coming under pressure to make a statement to MPs late on Friday. Labour’s health spokesman, Jonathan Ashworth, quoted in the Daily Mail, said: “Given this latest tragic news, it’s vital the health secretary provides a full oral statement to MPs in the Commons on Monday.” The paper reported that the Lib Dem health spokesman, Baroness Jolly, had also written to Hancock seeking answers.

Listeria infection is rare and usually causes a mild illness in healthy people. However, it can have more serious consequences among those with pre-existing medical conditions, pregnant women and those with a weak immune system.

The Good Food Chain said: “Our thoughts and deepest sympathies are with the families of those who have died and anyone else who has been affected by this outbreak. The underlying cause of it remains unclear.

“We understand that the investigations being carried out are complicated and will involve a number of stakeholders, but we hope the authorities will pursue their inquiries with all urgency so the wider industry can learn any lessons as soon as possible, and so those affected do not have to wait too long for answers.

“For our part, we are cooperating fully and transparently with the FSA and other authorities, and will continue to do so.”

North Country Cooked Meats said previously: “At this stage the company is currently co-operating fully with the environmental health and the FSA in their investigations, and a further statement will be issued in due course.”