David Cameron flew abroad last night for a long-arranged trip to Africa leaving behind the carnage inside Britain's most important police force, tumult inside the news organisation with which he has closest links, and open disdain from his deputy prime minister, Nick Clegg, over his appointment of Andy Coulson to No 10.

The in-flight entertainment will have to be very good to calm his mood.

Aides in Downing Street contacted the prime minister's Virgin plane en route from Heathrow to South Africa just shortly before Sir Paul Stephenson announced he was stepping down as the UK's most senior police officer.

Downing Street aides, who had at one point considered cancelling the trip altogether at the height of the phone-hacking crisis last week, instead decided to cut it back from the planned four days to two.

Cameron – who flew out with 25 business leaders including Barclays chief executive Bob Diamond – will now just visit South Africa and Nigeria on Tuesday. Plans to visit Rwanda and Sudan have been scrapped.

Time has been found in the diary to allow No 10 aides – and possibly the prime minister – to watch the appearance by Rupert and James Murdoch tomorrow in front of MPs on a parliamentary select committee.

Cameron may also find time to reflect that his attempt last Friday to get a grip of the situation by announcing a judicial inquiry has clearly failed. The number of dead bodies on the stage is beginning to resemble the final scene of a Shakespearian tragedy.

The "firestorm" he himself described is still raging, and as the body count rises in the form of arrests or resignations, he looks increasingly exposed.

Every day as the crisis continues, his judgment, and that of the chancellor, George Osborne, in appointing the former editor of the News of the World Andy Coulson as his director of communications looks increasingly inexplicable.

It cannot help that the leader of the opposition, previously a politically ponderous flea of no consequence, has suddenly morphed into a fast-moving deadly bee.

Ed Miliband will be back on the attack, framing the crisis in terms of his call for a new responsibility agenda in which the old status quo is over.

The problems Cameron faces come from all directions. First, he appears to be facing the thinly-disguised wrath of a Met commissioner angry that he is being accused of an improperly contractual relationship with Neil Wallis, a former News of the World deputy editor, when the prime minister arguably insisted on an even less appropriate relationship with Coulson.

Moreover, Stephenson was implying, possibly for self-serving reasons, that he could not impart operational information to Cameron since he was too compromised with the chief suspects.

Secondly there is no evidence that the Conservative party either in the Home Office or in the London mayoralty of Boris Johnson took seriously the suggestion, repeatedly raised by Labour, that the connections between News International and the Met were unhealthy.

Theresa May, the home secretary and a woman of principle, who is to make a statement to the Commons today about the relationship between the Metropolitan police and Chamy Media, Neil Wallis's PR firm, repeatedly said it was an operational matter for the police to decide whether fresh evidence had emerged, and left it to them to say there was none.

Thirdly, the record of meetings between Cameron and News International executives released on Friday does not reveal a modernising prime minister governing in the national interest, but a victim of a vested interest. His meetings with News International executives in a year exceed those with all other news organisations put together. Not a single figure from the BBC was granted an audience. It is one of those assemblages of small facts that change the way a public figure is viewed.

Finally, he is trying to manage the implosion of a political alliance that brought him to power, including the support of News International. He cannot know what divisions, angry recriminations and betrayals will occur in the next year as the causes of the crisis are examined, and individual personalities, facing jail, seek to save their reputations.

Cameron's visit to the two largest economies in sub-Saharan Africa – to try to highlight the importance of creating a free trade area in Africa - is not the first time that he has chosen to embark on a foreign excursion at an inopportune time.

Labour ridiculed him while, as opposition leader in the summer of 2007, he was in east Africa at the same time as parts of his Oxfordshire constituency and other parts of the UK were under water. In February of this year, as popular uprisings placed a spotlight on the lack of democracy across the Arab world, Cameron was to be found banging the drum for British arm sales at the head of at trade delegation to the Gulf states. Last night, explaining why the African trip was not called off, a Cameron aide said: "This trip is very important. We are improving economic links with South Africa. It's important that we continue to do that."

The prime minister – who will bring a message that an African free trade area could increase GDP across the continent by more than it currently receives in aid – will fly home early to finalise the terms and membership of Lord Justice Leveson's inquiry into the media. But that message is likely to be overshadowed by Stephenson and the arrest yesterday of Rebekah Brooks, the former chief executive of News International, who entertained the prime minister at her Oxfordshire home over the Christmas period.

The prime minister will fly home late allow him to finalise the arrangements for Lord Justice Leveson's inquiry in four areas.

Just hours before Stephenson's resignation, Clegg, told the BBC that a growing public perception of police corruption was deeply concerning. "I'm incredibly worried about that … The fact that the public, their cynicism in politicians or the press might have deepened is perhaps not entirely surprising. I think when the public starts losing faith in the police, it's altogether much more serious and you know you really are in some trouble."

Announcing his resignation, Stephenson admitted he was doing so because of the speculation relating to the Met's links with News International, but also "in particular in relation to Neil Wallis".

The Guardian was preparing to publish a story about how Scotland Yard chiefs invited Wallis to apply for a senior communications post with the force, in a decision which Stephenson was aware of.

Stephenson dated his relationship to Wallis back to 2006, a meeting that took place in the context of the latter's work as a journalist. From October 2009 to September 2010, Wallis's part-time work at the Met involved strategic communications, advising the commissioner and assistant commissioner, John Yates, as the force said there was no need to reopen the investigation into phone hacking at the News of the World.

The Guardian understands Wallis was approached to apply for the two-day-a-month contract with the Met after discussions which involved the most senior figures in the force.