The Duke of Cambridge has said he will fully support his children if they were to be gay, promising it would be “absolutely fine by me”.

The Duke, who spoke as he visited a charity that helps homeless LGBT people, said his only concern would be for the additional challenges they may face as a result of public prejudice.

Saying he and the Duchess had already discussed how they would approach one of their children telling them they were gay, lesbian, bisexual or transgender, he emphasised his only concern would be for any “hate or persecution” they would endure, particularly as a result of their public positions in the Royal Family.

The father-of-three visited charity akt, the Albert Kennedy Trust, to officially open its new services ahead of the annual Pride in London parade and to mark the 50th anniversary of the Stonewall uprising.

Answering questions from young ambassadors for the charity, he spoke frankly from the position of a parent about the challenges still faced by those who identified as LGBT.

His words are the most candid from any member of the Royal Family in public on the topic to date. When he is one day king, the Duke will be head of the Church of England and is likely to become the head of a Commonwealth in which, to date, 37 countries have laws that criminalise homosexuality.