David Cameron has been blamed by some in the British media for suggesting that Pakistan exports extremism and for sucking up to his Indian hosts last week. And Charles Moore, former editor of the Daily Telegraph, thinks that it is hypocritical of Cameron to blame Pakistan, since Britain itself tolerates extremists.

Actually, Cameron said nothing new on Pakistan. The US secretary of state, Hillary Clinton, has repeatedly urged Pakistan to do more to stamp out extremists on its soil – and she did so again in Islamabad last month. Pakistan did not react by breaking off talks with Washington, as its spy chief has done with London this week. Nor did it protest loudly against Clinton's statements, as it has against Cameron's censure of its double-dealing on extremists.

This is because Islamabad cannot afford to push its relationship with Washington to the brink. The US has been its largest military and economic donor since the early 1950s – and by the late 1980s, the official British archives had revealed that London could never offer as much as Washington.

Threats to cancel talks with the US – or carrying out the threats – could cost Pakistan more than $1bn a year in aid, which it says it needs to quash extremists on its turf. But Britain is just another middle-ranking European country itching to get out of Afghanistan. It is not even the major troop contributor there, so Pakistani intelligence officials can shake their fists at Cameron. At the moment, however, it appears that President Asif Zardari will stick to his London schedule, shake hands and engage in dialogue.

At different levels – and in very different ways – "America" also explains why Cameron got little coverage in the Indian media, why Barack Obama will address the Indian parliament during his state visit in November, and why Cameron couldn't in July. No country in the world can offer India as much as the US economically, intellectually or militarily. The sale of 57 Hawk aircraft is simply not in the same league as the Indo-US civilian nuclear deal of 2006. And in 2008-9, Britain was only India's seventh-largest trading partner, below China, the US, the United Arab Emirates, Saudi Arabia, Germany and Singapore, but above Hong Kong, Belgium and Switzerland.

More generally, Indians do not carry American historical baggage. The US did not found an Indian empire, and imprison Mahatma Gandhi and Jawaharlal Nehru for 11 and nine years respectively for daring to demand independence.

Cameron's wish to reduce the number of non-EU students and immigrants in Britain will not enhance his appeal to Indians. Currently there are more than 34,000 students in Britain and just over 1.5m British subjects of Indian origin. But there are more than 100,000 Indian students in the US and more than 3 million American citizens of Indian origin. It is rare to meet an Indian who has not been a victim of racism in Britain. But an Indian in the US are more likely to tell you that he or she beat 500 white Americans and got the top job in a top American firm, and that more generally, Indians feel accepted as equals by Americans and have close American friends.

Indians do not have a British dream. Indians dream an American dream, not just of going to the US but of making their country jump from rags to riches, and finding a pot of gold at the end of the Indo-American rainbow. The national interests and resources of Britain, the US, India, Pakistan will shape their relationships. Cameron should not be criticised for understanding this obvious fact.