The government has signed two contracts to secure warehouse space for the storage of drugs as part of ‘no-deal’ Brexit planning but officials are still working to secure a third with just 11 weeks to go before the UK leaves the EU.

Details of the Department of Health’s work on one of the most sensitive areas of Brexit planning emerged as the government comes under intensive pressure to say which firms it is working with following controversy over a £13.8m contract given to a ‘start-up’ freight company to operate ferries in the case of no deal, and questions about the way it was allocated.

The chair of the public accounts committee, Meg Hillier, has condemned the secrecy around the allocation of Brexit-related contracts as “ridiculous” and said this week that she would be asking the National Audit Office to investigate about £75m worth of Brexit consultancy deals signed with companies such as Deloitte, Accenture and PwC.

Following queries by the Guardian, the Department of Health said that two contracts for warehousing had been signed shortly before Christmas and a third is expected to be signed “in the very near future”. It is understood officials hope this will be in the coming days or weeks.

The total cost is in the region of £10m, according to the DoH, which said it would publish the names of successful contractors when the tender process is complete and all contracts have been signed.

A claim by the secretary of state for health, Matt Hancock, that his department had paid for 5,000 industrial-sized refrigerators, appears not to have been entirely accurate, however. While the warehouses have refrigeration capacity, the department has not purchased individual fridges, the Guardian has been told.

Instead, a reply from one of Hancock’s ministerial deputies, Stephen Hammond, to a parliamentary question from the Liberal Democrat Norman Lamb stated that agreements had been signed for storage, including refrigerated storage, for around 5,000 pallets.

Hammond told the Labour MP Luciana Berger, who asked a separate question, that funding had been agreed on the condition that the additional medicine warehousing capacity was in place in time to accommodate stockpiled medicines by the beginning of February.

“To reassure participating companies, we have committed to treating all information received confidentially, securely and to using it only for the purposes of the department’s programme. That means not introducing information about a company or a specific medicine into the public domain,” he added.

However, Berger called for more details to be made public, adding: “There should be nothing to stop the government telling us who the refrigeration contracts are being awarded to, even if that does not tell us which medicines they will contain.

“The details we have been given so far are extremely open ended and I am particularly concerned after the debacle surrounding Seaborne Freight. We need to know who these contracts are being awarded to.”

Lamb, a former health minister, said meanwhile: “It is really horrifying to see the Department of Health spending a fortune on fridges when there are so many other pressing priorities.

“When we know that a ‘no-deal’ is absolutely avoidable, this is a scandalous waste of money. The government will be held responsible for the reckless waste of public money.”

Concerns have already been expressed that Britain is running out of food warehousing space as retailers and manufacturers rush to stockpile amid growing fears of a no-deal Brexit. The Guardian reported in November that frozen and chilled food warehouses are fully booked for the next six months, with customers being turned away, industry representatives said.