In principle, there is no reason why an active politician - one still involved in the cut-and-thrust of public life - should not also have a regular slot as a contributor to or even as a presenter of a television programme.

The Labour MP Diane Abbott appeared week-in, week-out on This Week, a late-night BBC discussion programme, chaired by Andrew Neil. She was the perfect foil to the other regular contributor, Michael Portillo. Although Portillo had been a Tory MP and Cabinet minister, he retired from the Commons at the time of the 2005 general election. And although Abbott was, and still is, a Labour MP, she was replaced on the programme when she announced her candidature for the leadership of the Labour party last year.

Earlier this month, Neil admitted (during a Radio 5 interview) that he would like her to rejoin Michael Portillo on the This Week sofa. But he also made it clear that this could not happen while Ms Abbott remained a member of the Shadow Cabinet.

Andrew Neil is quite right. As a member of the Shadow Cabinet, Diane Abbott is to all intents and purposes the holder of a public office. She cannot express (at any rate in public) an opinion that contradicts that held collectively by the Shadow Cabinet.

These matters go to the heart of what we mean by sound judgment and appropriate conduct in public life. They are understood by the vast majority of the British political class. But not by Ken Livingstone.

Press TV is a mouthpiece for a brutal, tyrannical regime

In March 2009, Mr Livingstone became a presenter on Press TV, earning (I understand) £500 per programme. Last September, for better or worse, he was chosen as the Labour Party's candidate for the mayoralty of London, a contest that will be decided by the capital's voters next year. Although (thankfully) not in Parliament, Livingstone is nonetheless, therefore, privileged to hold an official position in the Labour party. It does not seem to have occurred to him that he should therefore cease presenting for Press TV. It does not seem to have occurred to Labour leader Ed Miliband that he should insist on Ken Livingstone cutting his contractual ties with Press TV. And it does not seem to have occurred to Press TV that it should bring these contractual ties to an end, at least until after the May 2012 mayoral contest.

If Livingstone had been presenting for BBC television we can be sure that his contract would have been terminated at once following his selection as a mayoral candidate. But Press TV is not the BBC. Press TV, on which I occasionally appear at a fee of between £50 and £75 (I made five appearances last year) is an arm of the Iranian government. It is in point of fact the English-language mouthpiece of a brutal and tyrannical regime characterised by a totally unashamed espousal of Holocaust denial and more general anti-Jewish prejudice.

It deliberately under-reports the gross abuses of human rights that are daily occurrences in the Iranian theocracy. Its UK operations are, it is true, constrained by the need to conform to the requirements of English law and to the jurisdiction of the media regulator, Ofcom, which has on three occasions upheld complaints against it.

In its favour, I can say that I am always treated courteously by its staff and presenters and that I have never been censored. At its London studios, I can present views that its considerable following in the Muslim world might not otherwise get to hear, and challenge the more outrageous lies and half-truths mouthed by other guests. But I hold no illusions about the station or its mission. And of course I am neither a programme presenter nor a candidate for public office.

Ken Livingstone is both. It is all very well for him to defend himself by saying (as he did on BBC television on January 19) that Press TV "is one of the few TV channels anywhere in the West that fairly presents the Palestinian case." By the very fact of defending himself in this way he gives the game away.

Obviously, we cannot expect a display of mature judgment from Mr Livingstone. But we have a right to expect it from his party leader, Ed Miliband. Mr Miliband should summon Mr Livingstone to his presence and tell him that his employment by Press TV is simply incompatible with his candidature for the most important post in British local government.