Media regulator Ofcom said that the comments made on the Radio Asian Fever community station were "likely to encourage or to incite the commission of crime or to lead to disorder".
This relates to two episodes of the programme Sister Ruby Ramadan Special 2011, aired in August last year, and broadcast in Urdu.
Presenter Rubina Nasir, also known as Sister Ruby, opened the programme with a Qur'anic verse (Sura Al-Nisa, verse 16) and gave her interpretation of this as being highly critical of mixed-faith marriages, but also homosexuality.
The presenter went on to discuss various historical events portrayed in the Qur'an in the context of her main discussion of homosexuality.
At one stage, she said: "What should be done if they do [practise homosexuality]? If there are two such persons among you, that do this evil, the shameful act, what do you have to do? Torture them; punish them; beat them and give them mental torture."
During the programmes, she added: "Allah states, 'If they do such a deed [i.e. homosexuality], punish them, both physically and mentally'. Mental punishment means rebuke them, beat them, humiliate them, admonish and curse them, and beat them up. This command was sent in the beginning because capital punishment had not yet been sent down."
Ofcom considered that these two particular statements "could be objectively and reasonably regarded as not only condoning but encouraging violent behaviour against homosexual people".
As acts of violence and hatred on grounds of sexual orientation are prohibited in the UK, the regulator considered that the broadcast of the statements was "likely to encourage or incite the commission of crime".
The Radio Asian Fever Community Interest Company must now pay a £4,000 fine to the HM Paymaster General, and broadcast a statement of Ofcom's findings, on a date and in a form to be determined by Ofcom.
But despite the severity of the breach, the regulator said that it "would not be appropriate to shorten, suspend or revoke Radio Asian Fever's licence".
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