And so it was that a huge party of ministers and businessmen accompanied the Prime Minister to the sub-continent, talking about contracts, green initiatives and universities.
But, by Wednesday, things were not going quite right. I was struck by a juxtaposition of stories in this newspaper. One carried the headline: "Gaza is like a prison camp, says PM." Next door, was a report in which Mr Cameron proclaimed that he was approaching India with "humility". Although the Gaza remarks were made in Turkey, not India, the stories did not sit happily together. Was Mr Cameron being blunt or humble? It's hard to be both at once.
When he actually reached India, he did not lower the temperature. Speaking in Bangalore, he said that "we cannot tolerate the idea that this country [Pakistan] is allowed to look both ways and is able… to promote the export of terror". The new Foreign Secretary, William Hague, tactfully explained that the Prime Minister "wasn't accusing anyone of double-dealing". But anyone not trained as a politician or diplomat could see that he was.
Faced with protests, Mr Cameron decided to defend himself. He was simply an honest man abroad, was the line. The British people, he said, did not expect him "to go around the world telling people what they wanted to hear".
Yet the fault in his "gaffes" had something to do with the fact that he was telling his immediate audience what it wanted to hear. In saying that Gaza was a "prison camp", without even mentioning Hamas, he was repeating the line of his host, the Turkish prime minister, Recep Erdogan. Mr Erdogan recently said: "I do not accept Hamas as a terrorist organisation", and one Hamas leader declared: "Mr Erdogan has become our voice." Everything, for Mr Erdogan and for Hamas, is the fault of Israel. Mr Cameron seemed to endorse this.
Who was annoyed? Israel, obviously. The United States, too: even President Obama, who is cooler than his predecessors towards Israel, does not want to lessen pressure on Hamas, and his administration is considering whether to ban the IHH, the organisation which led the famous "peace" flotilla to Gaza, because of its alleged links with terrorism. Mr Cameron's remarks also upset Egypt, which is the other guard of what he calls the Gaza "prison camp", and is in constant conflict with Hamas.
And they were unwelcome to all those in Turkey who are most keen to preserve the democratic secularism of the state. Far from producing a happy marriage of civilisations ("East and West together", chirped Mr Cameron), Mr Erdogan's Islamic AKP party has driven Turkey further from plural European democracy, closer to Iran and to the violent Muslim Brotherhood doctrines which see the West as the enemy. Turkey's Islamists must be thrilled to be told by a Western leader that, in Afghanistan and the Middle East, they have "a credibility that others in the West just cannot hope to have". So must we accept that their support for Hamas is credible, even creditable, too, and will enable Turkey, as Mr Cameron asks, to "make the case for peace" with nasty old Israel? Turkey should come into the EU, he says, because "it is just wrong to say that it can guard the camp but not be allowed to sit inside the tent", How good is the guard if he is fraternising with the enemy?
In linking Pakistan with terrorism, Mr Cameron was – unlike in what he said about Gaza – relaying facts. From his own security sources, he knows (not suspects, but knows) that Pakistani official agencies had a hand in the Mumbai attacks and in Taliban operations. It is one of the most serious problems in the world. But was it a good idea to deploy this fact to schmooze his Indian hosts? When one says something highly unpleasant, in public, about one's ally, one must do so face to face, for a good reason, and to produce a definite result. This rule was not followed. Mr Cameron's words won't even get an extra call-centre contract in Bangalore, let alone a Pakistani change of heart.
A spokesman defended Mr Cameron's attack on Pakistan by pointing out that he had intended to attack not the government, but the country. In diplomacy, which is the art of inter-state relations, it is not easy wholly to separate one from the other. Besides, it strikes me that the Prime Minister's criticism of the ability to "look both ways" in relation to terrorism also applies to another important country – the United Kingdom of Great Britain and Northern Ireland.
When he was Leader of the Opposition, Mr Cameron often said in conversation that there was something crazy about our running round the world trying to fight the "war on terror" while allowing hate preachers to operate untrammelled at home. Early on, his Government took a good decision in this spirit, when the Home Secretary, Theresa May, bravely defied strong pressure and refused entry to this country to Zakir Naik, a sectarian Islamist preacher. Mr Cameron's natural common sense is strong on this sort of issue.
Yet the fact remains that the Coalition has inherited a deep confusion from the last government, which it has not yet resolved. In the official programmes, such as Prevent, designed to counter Islamist extremism, powerful "voices of conservatism" continue to urge that it is the extremists themselves, so long as they do not advocate actual violence here, who should get public money and support. So right here, now, in Britain, supporters of Hamas, of the killing of homosexuals, of female circumcision, of the execution of apostates, and of terrorism against all armed opponents of any Muslims anywhere, are treated as "partners" by police and other public authorities to help restrain radicalism.
After the July 7 bombings in 2005, Tony Blair told Pakistan to do something about its extreme madrassas (religious schools). He was right; but the not unreasonable reply came back: "What about your madrassas?" Even today, Britain tolerates terror, as Mr Cameron complains about Pakistan, so long as it is an export business.
So we are in a muddle, one which Mr Cameron's intercontinental frankness this week unintentionally exposed.