THE old rules still apply in the unprecedented scandal shaking the British press, police and political establishment, starting with the dictum: in public life, it is cover-ups that hurt more than the original crimes.

That is why it is wrong to argue, as do some Labour MPs, some bloggers and tonight's edition of BBC Newsnight, that David Cameron logically might have to resign as prime minister, now that Britain's most senior police officer, Sir Paul Stephenson, has had to quit.

The argument rests on a superficially neat piece of symmetry. Sir Paul, until this weekend Commissioner of the Metropolitan police, had to resign after it emerged that his force had employed the former deputy editor of the News of the World, Neil Wallis, as a PR consultant. In contrast, Mr Cameron hired Mr Wallis's boss, the ex-NotW editor Andy Coulson as his PR chief, and yet he is still in his job as prime minister. "Spot the Difference", grumbled the Newsnight political editor Michael Crick, who had earlier asked the Tory mayor of London, Boris Johnson, to explain the same contrast at a press conference this afternoon, reducing the normally loquacious Mr Johnson to stammering and flannelling.

Ex-commissioner Stephenson clearly sees things the same way, aiming a clear barb at Downing Street in his resignation statement, when he noted that his ex-tabloid helper had never had to resign, unlike the prime minister's ex-tabloid helper, Mr Coulson (who stood down as editor of the NoTW in 2007 after the jailing of his royal correspondent and a private investigator over phone-hacking, even though he said he knew nothing about it).

But the problem was not so much that Neil Wallis was given a two day a month contract at Scotland Yard between 2009 and 2010, advising senior officers on PR strategy. The problem is that more recently, even after the police came under huge pressure for their astonishingly lackadaisical approach to the phone-hacking scandal at the NotW, senior officers did not think it appropriate to tell anyone in government, let alone the public, that they had been paying a former deputy editor of the same paper for strategic press advice.

This though that advice was being given at the very same time, in 2009, when Scotland Yard was deciding not to reopen the hacking investigation, and was poo-pooing the excellent reporting of the scandal by papers like the Guardian. In the end, the police only alerted the government last week, on the day that Mr Wallis was arrested on suspicion of involvement in phone hacking, as part of the current police probe, known as Operation Weeting.

If it had only just emerged that David Cameron had been secretly taking paid advice from Andy Coulson, the prime minister would also be in astonishing trouble right now. As it is, Mr Coulson's appointment (which was a colossal mistake, as I have said many times) was a matter of public record. That makes a very big difference.

To be fair, Sir Paul has an explanation, saying:

In 2009 the Met entered into a contractual arrangement with Neil Wallis, terminating in 2010. I played no role in the letting or management of that contract. I have heard suggestions that we must have suspected the alleged involvement of Mr Wallis in phone hacking. Let me say unequivocally that I did not and had no reason to have done so. I do not occupy a position in the world of journalism; I had no knowledge of the extent of this disgraceful practice and the repugnant nature of the selection of victims that is now emerging; nor of its apparent reach into senior levels... ...Now let me turn to the reported displeasure of the Prime Minister and the Home Secretary of the relationship with Mr Wallis. The reasons for not having told them are two fold. Firstly, I repeat my earlier comments of having at the time no reason for considering the contractual relationship to be a matter of concern. Unlike Mr Coulson, Mr Wallis had not resigned from News of the World or, to the best of my knowledge been in any way associated with the original phone hacking investigation. Secondly, once Mr Wallis's name did become associated with Operation Weeting, I did not want to compromise the Prime Minister in any way by revealing or discussing a potential suspect who clearly had a close relationship with Mr Coulson. I am aware of the many political exchanges in relation to Mr Coulson's previous employment - I believe it would have been extraordinarily clumsy of me to have exposed the Prime Minister, or by association the Home Secretary, to any accusation, however unfair, as a consequence of them being in possession of operational information in this regard. Similarly, the Mayor. Because of the individuals involved, their positions and relationships, these were I believe unique circumstances.

The assistant commissioner of the Met, John Yates, who took the decision in 2009 not to re-open the phone-hacking probe and who also resigned today, has an explanation to offer too:

We in the Police Service are truly accountable. Those of us who take on the most difficult jobs clearly have to stand up and be counted when things go wrong. However, when we get things wrong, we say so and try and put them right. As I have said very recently, it is a matter of great personal regret that those potentially affected by phone hacking were not dealt with appropriately. Sadly, there continues to be a huge amount of inaccurate, ill-informed and on occasion downright malicious gossip published about me personally. This has the potential to be a significant distraction in my current role as the national lead for Counter Terrorism. I see no prospect of this improving in the coming weeks and months as we approach one of the most important events in the history of the Metropolitan Police Service, the 2012 Olympic Games. The threats that we face in the modern world are such that I would never forgive myself if I was unable to give total commitment to the task of protecting London and the country during this period. I simply cannot let this situation continue.

Sadly, readers will note that both these explanations, though differing in tone and content, share one important quality: neither begins to make any sense at all.