Transgender women have had their right to use Hampstead Heath ponds formalised in a new policy.

The City of London Corporation (CoLC), which manages Hampstead Heath and its ponds, announced that it had adopted a new gender identity policy to make sure services in the area “are fully compliant with the Equality Act 2010, and do not discriminate against trans people”.

In January, the City of London, confirmed that the ladies’ pond – which counts people such as the actor Helena Bonham Carter and novelist Esther Freud among its swimmers – was open to transgender women. That was formalised in an announcement on Thursday that the new rules would “ensure a robust and consistent approach to gender identity”.

The corporation has previously said that trans women have been able to use the Kenwood Ladies’ Pond since the introduction of the Equality Act 2010, which prohibits unlawful discrimination on the grounds of transgender status.

Edward Lord, the chair of the establishment committee, which leads on the CoLC’s workforce and inclusion policies, said: “All communities should be fully respected, and equality and basic human rights upheld.”

A statement on the CoLC website said the new approach would “minimise potential issues of exclusion and discrimination”.

The announcement comes after a consultation on attitudes to gender identity held last year received nearly 40,000 responses, of which 21,191 were deemed valid. CoLC said 65% of those valid respondents favoured ensuring trans people did not suffer discrimination.

Thousands of responses to the consultation were deemed invalid on the basis that the respondents did not answer any questions.

The consultation was accompanied by an intense debate. In May last year women went into the heath’s men-only pond, some dressed in fake beards, claiming that a policy based on how people identify themselves was open to abuse. Meanwhile LGBT charity Stonewall attacked a “toxic” media debate around the issue, pointing out that the Equality Act 2010 already said trans people should be allowed to access single-sex spaces that match their gender without discrimination.

The Kenwood Ladies’ Pond Association said: “The Ladies’ Pond is a single-sex space and the KLPA is committed to helping to create there an inclusive environment for all women, including transgender women, which is free from discrimination, harassment or victimisation.”

In February last year members of the pond met to discuss their position on the inclusion of trans women.

The KLPA said on Thursday it welcomed transgender women as members.