NHS bosses are scrambling to overhaul guidelines for single-sex spaces in thousands of hospitals and GP surgeries after the equality watchdog warned they would be pursued if they fail to do so.

The British Transport Police became the first to change policies on Thursday amid the fallout from the supreme court ruling on the legal definition of a woman, piling pressure on the health service and other organisations to revamp their guidance.

Current NHS guidance in England says trans people should be accommodated based on how they dress, their names and their pronouns. Under Wednesday’s ruling that a woman is defined by biological sex under the Equality Act 2010, this would be scrapped.

Senior NHS legal officials and estates and facilities managers are racing to draw up proposals for how hospitals, community care centres and GP practices should reflect the ruling, sources told the Guardian.

The ruling poses a challenge for the NHS, which has an estate spanning 25m square metres in England alone, with infrastructure repair bills of more than £14bn. The issue is further complicated by the fact that health policy and spending is devolved in Wales and Scotland.

Kishwer Falkner, the chair of the Equality and Human Rights Commission (EHRC), told BBC Radio 4’s Today programme on Thursday: “They [the NHS] have to change it. They now have clarity.

“There is no confusion as of yesterday, at 10.30 in the morning, and they can start to implement the new legal reasoning and produce their exceptions forthwith, but they have to change it. We will be having conversations with them to update that guidance.”

Asked if the EHRC would pursue the matter if the NHS did not do so, she replied: “Yes, we will.”

An NHS England spokesperson said: “The NHS is currently reviewing guidance on same-sex accommodation and, as part of this process, will consider and take into account all relevant legislation and [Wednesday’s] ruling.”

Meanwhile, the BTP, which patrols the railways in Great Britain, announced that male officers would conduct intimate searches of trans women “in accordance with the biological birth sex of the detainee”, while trans men would be searched by female officers.

Under the force’s previous policy, officers had been told that anyone in custody with a gender recognition certificate would be searched by an officer matching a detainee’s acquired gender.

The update comes during a legal battle between gender-critical campaigners and the force over its guidance that allowed transgender officers to strip-search women, so long as the officer held a gender recognition certificate.

The rapid change of approach came after Lady Falkner said the EHRC would be issuing updated and legally binding codes of practice on single-sex spaces and services in the wake of the “enormously consequential” court ruling.

“We are going to have a new statutory code of practice [meaning] it will be interpreted by courts as the law of the land. We’re hoping we’re going to have that by the summer,” she told Today.

She said the judgment meant only biological women could use single-sex changing rooms and women’s toilets, or participate in women-only sporting events and teams, or be placed in women’s wards in hospitals.

Even so, the commission “will not tolerate” discrimination or harassment of trans people, which remains unlawful under the Equality Act, and would support trans women taking out equal pay claims under sex discrimination laws.

Falkner said the ruling was “a victory for common sense” but “only if you recognise that trans people exist, they have rights and their rights must be respected. Then it becomes a victory for common sense.”

The UK government has avoided making any substantial comment on the ruling, but a strong indication of Labour’s approach came from Anas Sarwar, the Scottish Labour leader, who swung the party behind the supreme court and the EHRC’s stance.

Previously a supporter of self-identification for trans people, Sarwar said there was now a need for an “urgent” update of Scotland’s policies on single-sex spaces. Scottish ministers are expected to update Holyrood next week on their response to the ruling.

“I’ve always said that we should protect single-sex spaces on the basis of all biological sex,” he said during a visit in Falkirk. “There’s a clear ruling now from the supreme court.”

The bulk of the reaction from Westminster politicians continued to come from the Conservatives. Speaking during a local elections campaign visit to Cambridgeshire, Kemi Badenoch, the Tory leader, said the court decision was a vindication of their views.

She said she would support changes to the Equality Act and Gender Recognition Act to cement the court’s view. “These laws were written 20 years ago plus when the world was different. A lot of people are trying to change what the law means,” she said.

In contrast, there was little sign of how ministers will help institutions navigate the new framework. Rachel Reeves, the chancellor, on a visit to Scunthorpe, dodged some questions on the issue, saying only that more advice would come in “due course”.

Among the issues that will need to be tackled is provision of toilet facilities for transgender people, given the EHRC said the ruling means they will not be able to use single-sex toilets.

A directive introduced by Badenoch when she was equalities minister last year requires new public buildings such as offices and shopping centres to prioritise single-sex toilets, and to provide universal toilets only “where space allows”.

That regulation remains in force, meaning public buildings could become increasingly inaccessible for transgender users.