In almost every way, David Headley was the perfect neighbour. When the 49-year-old American citizen began renting an apartment in Mumbai last year he charmed his landlord, treated his laundry boy with respect, and befriended Bollywood figures at a local gym.

He told them that he was Jewish, and running an immigration agency from a respectable part of town. “Sweet and charming,” said his landlady. “Down to earth,” said his personal trainer.

Not until the past few days did they learn of his alleged other identity — and of quite how close security figures claim India may have come to a repeat of the militant attacks on Mumbai a year ago next week.

Apparently, Mr Headley’s original name was Daood Gilani. He was born in Pakistan, and is suspected of helping the terrorists who carried out last year’s Mumbai attack, and of planning another atrocity this year.

The details emerged when the FBI arrested Mr Headley in his home city of Chicago on October 3, and filed an affidavit in a US court, which has since been made public.

It alleges that he worked with Harkat ul-Jihad al-Islami (Huji), a Pakistan militant group, and Lashkar e-Taiba (LeT), the Pakistan group blamed for last year’s Mumbai attacks. The document also outlines claims that he was involved in the “Mickey Mouse Project” — a plan to attack Jyllands-Posten, the Danish newspaper whose cartoons depicting the Prophet Muhammad in 2005 infuriated Muslims across the world.

It also allegedly shows that he and an apparent accomplice visited India several times between 2006 and 2009, and appear to have discussed attacking Indian targets as recently as September this year.

Indian investigators are now examining whether Mr Headley may be the “missing link” in the Mumbai attacks, which killed more than 170 people between November 26 and 29 last year. They are also investigating claims that he may have planned attacks this year on targets including the National Defence College in Delhi, the private Doon School in Dehradun, northern India, or even a nuclear facility.

In the process, they are shedding light on the evolving threat from LeT and its allies, and on India’s haphazard — but so far successful — efforts to respond. “This is yet another wake-up call for India,” said B. Raman, a former counter-terrorism chief in the Indian external intelligence service, the Research and Analysis Wing.

“This shows LeT is as determined as ever to attack India, and they are now using Western territory and foreign Muslims to do it.”

The most striking aspect of the Headley case is his profile: unlike other militant suspects, he is middle-aged, speaks fluent English, and lives in Chicago.

The son of a Pakistani diplomat and an American woman, he went to cadet college in Pakistan before moving to the US when he was 16.

In 1997, he was jailed for 15 months for trying to smuggle heroin into the US, according to court documents.

Yet by simply changing his name in 2006, he stayed under the radar on at least nine visits to India over the past three years.

The FBI says that in the alleged activities he was helped by Tahawwur Hussain Rana, a Canadian citizen of Pakistani origin who studied at the same cadet college, and was also arrested in the US last month.

Mr Rana’s immigration agency, which has offices in Chicago, helped to arrange Mr Headley’s trips and provided his cover story, according to the FBI.

To burnish his fake Jewish credentials, Mr Headley even carried a book called How to Pray like a Jew, the FBI says. The FBI appears to have placed him under surveillance after noticing his frequent movements between India, Pakistan, the Gulf and Europe.

It alerted Indian authorities after intercepting an e-mail in which Mr Headley’s alleged handler appears to give him a coded message suggesting an attack on India.

“I need to see you for some new investment plans,” the affidavit quotes the handler as saying.

When Mr Headley asks where, the handler suggests that he should “say hi to Rahul” in what the FBI says is a reference to a prominent Indian actor.

The actor has since been identified as Rahul Bhatt, a minor Bollywood star, who has admitted befriending Mr Headley in Mumbai.

In a telephone intercept in September, Mr Headley and Mr Rana are heard discussing five alleged targets and mentioning “Defence College”, according to the affidavit.

Mr Headley and Mr Rana have yet to respond to the affidavit.

But Indian and Western officials and analysts agree that the evidence presented so far appears to underline the global reach and ambitions of Huji and LeT. It also confirms India’s long-held fears that such groups might use foreigners of Pakistani or Indian origin, forcing it to tighten visa procedures.

Western governments had already adapted to that threat, but are worried that Mr Headley and Mr Rana may have used their immigration agency to move militants around the globe.

They are also increasingly aware of the threat to their own citizens in India — particularly during next year’s Commonwealth Games in Delhi.

“Prior to Mumbai, LeT was largely seen as a regional threat,” said one Western diplomat.

“Mumbai brought home that attacking India could directly impact Western interests, by killing their nationals, and also their indirect interests by destabilising the region.”

There is less agreement, however, on what the case says about India’s domestic security.

Some say that LeT and its allies are becoming more desperate as the Pakistan Army — which once sponsored them — has become distracted by its own campaign against the Taleban.

India has also taken a number of steps to improve its security apparatus. It has, for example, now established the National Investigation Agency, and it is amending legislation to give increased powers to the security services.

P. Chidambaram, the new Home Minister, has now started chairing a meeting of the heads of all the country’s important security agencies every morning.

The National Security Guard — whose commandos took eight hours to get to Mumbai from their Delhi headquarters last year during the attacks — has expanded its numbers and set up hubs in four more cities, including Mumbai.

“What about the past, almost 365, days?” said J. K. Dutt, the former NSG chief who led last year’s Mumbai operation. “There haven’t been any terrorist attacks since Mumbai. Doesn’t that also speak of the fact that there are steps the country has taken?”

Critics, however, say that India had a lucky escape thanks only to the FBI. Others question whether the US should have informed India earlier that it was watching Mr Headley.

Yet the biggest concern of all is still the underfunded and short-staffed police, a force which under India’s Constitution is the responsibility of state governments.

“When are we going to improve the training, consciousness and capability of local police?” asked Arun Bhagat, a former head of the Indian Intelligence Bureau. “Central agencies can only do so much.”

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