The Equality and Human Rights Commission (EHRC), which regulates the Equality Act, subsequently issued interim guidance saying that companies should no longer allow trans women into female-only facilities. It said this would “mean that they are no longer single-sex facilities and must be open to all users of the opposite sex”.

Like other companies, the Co-op is now looking at what this means for its HR policies. An initial assessment has found that single-sex spaces are available in most of Co-op’s locations, but the sprawling nature of the business means there are challenging areas. The Co-op runs more than 2,300 convenience stores, more than 800 funeral parlours and has insurance, legal and wholesale teams in the UK.

Ms Khoury-Haq said “the key areas that we will need to look at differently are changing rooms”, which are in funeral branches, funeral care centres and depots.

Some companies have already begun updating policies. Barclays, for example, has banned trans women from using female lavatories, reversing an earlier policy of allowing them to use whichever bathroom they feel most comfortable in.

However, Co-op has said it will wait until the EHRC publishes full guidance, expected in June, and until then will allow staff to “continue to use toilets and changing facilities in accordance with their gender identity.”

Ms Khoury-Haq’s staunch support of trans staff risks attracting attention from gender-critical campaigners, who for years have accused companies of promoting trans ideology under the banner of equality.

She said Co-op would continue to be a “safe place for people, where they can do a great job but also be themselves”, adding: “If that’s ‘woke’, I’m fine with it.”

Co-op follows Lloyds Bank in vowing to stand behind trans staff in the wake of the Supreme Court ruling. Britain’s biggest lender has pledged “solidarity” with transgender staff.

Ms Khoury-Haq said: “On a personal level, I need to take care of my trans colleagues. I always will, and, as long as I’m there, they will be protected. I will absolutely protect those people to the end.”

The Supreme Court ruling on the definition of gender is one of many fast-moving issues Co-op’s chief has to navigate. Just hours after sitting down with the Telegraph, Ms Khoury-Haq was told by her IT team that the company was the victim of an attempted hack.

Some back-office and call-centre systems were quickly taken down as part of “proactive steps to keep systems safe”.

Attempted security breach

In a letter to staff, Co-op said security was of “paramount importance” given the “recent issues surrounding M&S and the cyber attack they experienced”.

On Friday, Co-op admitted that hackers had breached its systems and stolen data “relating to a significant number of our current and past members.” While financial data is not thought to be included, cyber attackers have accessed people’s names and contact details. Hackers claimed to the BBC that had details on 20 million Co-op members, though the retailer has not confirmed the number.

The cyber attack came in the wake of the crippling IT breach that has plagued Marks & Spencer for the past two weeks. Co-op declined to provide any additional comment on the incident. It said Ms Khoury-Haq would not be able to speak about the breach.

Speaking last week, the Co-op chief said she was planning to add more technology to shops to help offset the £150m in extra costs hitting the business this year. This includes rolling out electronic shelf labels, where prices are displayed virtually and can be updated more easily.

“There’s a heavy burden on business at the moment when you look at it across the board,” Ms Khoury-Haq said. “When labour is much cheaper, it’s hard to make a business case for a large-scale technology rollout, but when labour is more expensive, that business case starts to look very different.”

Collectively, retailers face £7bn of extra costs as a result of Rachel Reeves’s tax raid last October. The rise in the minimum wage and National Insurance changes that took effect on April 1 mean the cost of employing a worker in an entry-level retail job has risen by 10pc.

Ms Khoury-Haq wants ministers to do more to help retailers, rather than simply piling on extra costs. She said: “We’ve been saying to ministers, if you can help us reduce the loss from our stores, then the National Insurance becomes something that we can balance.”

A shake-up of business rates would help the majority of Co-op stores but that is still some way off.

In the meantime, retailers have been hit by a recycling levy forecast to cost the industry £2bn. Ms Khoury-Haq tried to make the case for this to be delayed “but they decided to bring it in anyway”.

The wave of costs have already started to feed into higher prices. Last month, food inflation rose to its highest level in 11 months, according to the British Retail Consortium. Ms Khoury-Haq said Co-op will “absorb as much as we possibly can, as we have been all along, to keep prices as low as possible”.

Aside from the Co-op, Ms Khoury-Haq also co-chairs the Net Zero Council alongside Ed Miliband, the Energy Secretary, reprising a role she held with the previous government. The advisory group was set up to help businesses and the Government work together on net zero as Britain races to decarbonise its energy system by 2030.