Foreign Secretary Jeremy Hunt said dual nationals face an “intolerable risk of mistreatment” and arbitrary detention.
And Iranians with links to British institutions are also at risk of falling under suspicion in Iran, the advice adds.
It comes after British Council worker Aras Amiri was jailed for spying.
The Iranian national, who was arrested while on a visit to see her ill grandmother, was sentenced to 10 years in prison in Iran on Monday.
The Foreign Office updated its advice on Friday.
Mr Hunt also warned that Iranian nationals living in the UK should exercise “caution” when returning to Iran to visit family and friends.
“Dual nationals face an intolerable risk of mistreatment if they visit Iran,” Mr Hunt said.
“Despite the UK providing repeated opportunities to resolve this issue, the Iranian regime’s conduct has worsened.
“Having exhausted all other options, I must now advise all British-Iranian dual nationals against travelling to Iran.”
Mr Hunt added: “The dangers they face include arbitrary detention and lack of access to basic legal rights, as we have seen in the case of Nazanin Zaghari-Ratcliffe, who has been separated from her family since 2016.”
Mrs Zaghari-Ratcliffe, a dual British-Iranian national, is serving five years in prison for spying – a charge she denies.
According to the BBC’s diplomatic correspondent, James Robbins, the Foreign Office seems to have concluded that prospects for her release have worsened, and that people who live in Britain who have connections to the country are now at even greater risk of being arrested and then jailed for long periods.
For British nationals, the advice is to consider carefully the risks of travelling to Iran.
The Iranian government does not recognise dual nationality, considering dual British-Iranian nationals as Iranian citizens.
The new travel advice comes as tensions between Tehran and the West – in particular the US – have heightened in recent times.
Source » bbc