Formal guidance on how organisations should implement the supreme court ruling on gender may not be fully signed off for months, officials and MPs have warned, amid increasing worries about the capability of the government’s equalities watchdog.

While the Equality and Human Rights Commission (EHRC) has promised to complete the process by the end of July, a series of insiders have told the Guardian they believe this may not happen until after the watchdog’s controversial chair, Kishwer Falkner, is replaced in November.

Some MPs are increasingly worried about what one said could be months of “limbo” for organisations and transgender people.

The concerns are in part due to worries about the ability of Lady Falkner, who was appointed by Liz Truss, to be seen as a fair arbiter of how public bodies should implement the court decision that “woman” in the Equality Act refers only to a biological woman.

The guidance will attempt to navigate a path for the parallel needs and rights concerning single-sex spaces such as toilets, changing rooms and associations, as well as for transgender people, many of whom fear the supreme court ruling could effectively exclude them from the public realm.

Officials also expect a high volume of submissions to the six-week consultation process, with some predicting thousands of responses, which could swamp the relatively thinly staffed organisation.

“I just don’t get the sense the EHRC has the resources to get this done quickly,” one MP with a close interest in the process said. “We don’t want a rushed job, but at the same time, you can’t keep public organisation – and transgender people – just waiting for months. This is a bigger issue than Falkner, but she isn’t a help.”

In April, the EHRC released interim, non-statutory advice about how to interpret the ruling, which set out that transgender people should not be allowed to use toilets of the gender they live as, and that in some cases they cannot use toilets of their birth sex.

A number of critics have called the advice oversimplistic. One Labour MP said: “A lot of lawyers told me it is utterly ridiculous, and the supreme court judgment does not necessarily mean that.” Some government officials are also worried, with one saying the EHRC had “bungled” the advice.

Falkner, a crossbench peer, is seen as having led closely on the interim advice. Some EHRC sources said most senior staff had no idea it had even been drawn up until it was published on the organisation’s website late on a Friday evening.

The EHRC initially set a two-week timetable for consulting on the full guidance, but changedthat to six weeks after concern from the Commons women’s and equalities committee.

While Falkner and the EHRC will be responsible for drawing up the formal guidance, this must then be signed off by the government, and some believe it could end up not being in place before Falkner is replaced.

Last November she was given a 12-month extension on her four-year term. Harriet Harman, the Labour former cabinet minister who introduced the 2010 Equality Act to parliament, has been named as a possible successor.

While a number of MPs believe Harman could do a better job, such a long delay in setting out how organisations should respond to the supreme court would risk months of confusion for them, and significant worry for transgender people.

“Most public bodies don’t know what to do,” another MP said. “The government is frozen and waiting to see what the EHRC says. But I don’t think we’ll get anywhere with Falkner as chair. She’s not neutral.

“Unless ministers are confident that all voices are being heard they won’t sign off on the guidance, and they are watching this very closely. It’s currently a bit of a mess.”

John Kirkpatrick, the EHRC’s chief executive, said the interim update was “issued in response to a high level of demand for accurate information following the judgment”, and that Falkner had been “visible in providing clarity on the consequences of the judgment on behalf of the EHRC”.

He added: “Like all well-governed organisations, we have robust decision-making processes and internal channels through which colleagues can escalate concerns. We do not recognise the views attributed to ‘insiders’ as being representative of our staff.”