Lawyers and intelligence experts with direct knowledge of two intercepted terrorist plots that the Obama administration says confirm the value of the NSA's vast data-mining activities have questioned whether the surveillance sweeps played a significant role, if any, in foiling the attacks.

The defence of the controversial data collection operations, highlighted in a series of Guardian disclosures over the past week, has been led by Dianne Feinstein, chairwoman of the Senate intelligence committee, and her equivalent in the House, Mike Rogers. The two politicians have attempted to justify the NSA's use of vast data sweeps such as Prism and Boundless Informant by pointing to the arrests and convictions of would-be New York subway bomber Najibullah Zazi in 2009 and David Headley, who is serving a 35-year prison sentence for his role in the 2008 Mumbai attacks.

Rogers told ABC's This Week that the NSA's bulk monitoring of phone calls and internet contacts was central to intercepting the plotters. "I can tell you, in the Zazi case in New York, it's exactly the programme that was used," he said.

A similar point was made in anonymous briefings by administration officials to the New York Times and Reuters.

But court documents lodged in the US and UK, as well as interviews with involved parties, suggest that data-mining through Prism and other NSA programmes played a relatively minor role in the interception of the two plots. Conventional surveillance techniques, in both cases including old-fashioned tip-offs from intelligence services in Britain, appear to have initiated the investigations.

In the case of Zazi, an Afghan American who planned to attack the New York subway, the breakthrough appears to have come from Operation Pathway, a British investigation into a suspected terrorism cell in the north-west of England in 2009. That investigation discovered that one of the members of the cell had been in contact with an al-Qaida associate in Pakistan via the email address sana_pakhtana@yahoo.com.

British newspaper reports at the time of Zazi's arrest said that UK intelligence passed on the email address to the US. The same email address, as Buzzfeed has pointed out, was cited in Zazi's 2011 trial as a crucial piece of evidence. Zazi, the court heard, wrote to sana_pakhtana@yahoo.com asking in coded language for the precise quantities to use to make up a bomb.

Eric Jurgenson, an FBI agent involved in investigating Zazi once the link to the Pakistani email address was made, told the court: "My office was in receipt – I was notified, I should say. My office was in receipt of several email messages, email communications. Those email communications, several of them resolved to an individual living in Colorado."

Michael Dowling, a Denver-based attorney who acted as Zazi's defence counsel, said the full picture remained unclear as Zazi pleaded guilty before all details of the investigation were made public. But the lawyer said he was sceptical that mass data sweeps could explain what led law enforcement to Zazi.

"The government says that it does not monitor content of these communications in its data collection. So I find it hard to believe that this would have uncovered Zazi's contacts with a known terrorist in Pakistan," Dowling said.

Further scepticism has been expressed by David Davis, a former British foreign office minister who described the citing of the Zazi case as an example of the merits of data-mining as "misleading" and "an illusion". Davis pointed out that Operation Pathway was prematurely aborted in April 2009 after Bob Quick, then the UK's most senior counter-terrorism police officer, was pictured walking into Downing Street with top secret documents containing details of the operation in full view of cameras.

The collapse of the operation, and arrests of suspects that hurriedly followed, came five months before Zazi was arrested in September 2009. "That was the operation that led to the initial data links to Zazi – they put the clues in the database which gave them the connections," Davis said.

Davis said that the discovery of the sana_pakhtana@yahoo.com email – and in turn the link to Zazi – had been made by traditional investigative work in the UK. He said the clue-driven nature of the inquiry was significant, as it was propelled by detectives operating on the basis of court-issued warrants.

"You can't make this grand sweeping [data collection] stuff subject to warrants. What judge would give you a warrant if you say you want to comb through vast quantities of data?"

Legal documents lodged with a federal court in New York's eastern district shortly after Zazi's arrest show that US counter-intelligence officials had been keeping watch over him under targeted surveillance with the warranted approval of the special intelligence court. During the course of the prosecution, the US served notice that it would be offering evidence "obtained and derived from electronic surveillance and physical search conducted pursuant to the Foreign Intelligence Surveillance Act of 1978 (Fisa)."

Feinstein and Rogers have also pointed to the case of David Headley, who in January was sentenced to 35 years in jail for having made multiple scouting missions to Mumbai ahead of the 2008 terrorist attacks that killed 168 people. Yet the evidence in his case also points towards a British tip-off as the inspiration behind the US interception of him.

In July 2009, British intelligence began tracking Headley, a Pakistani American from Chicago, who was then plotting to attack Danish newspaper Jyllands-Posten in retaliation for its publication of cartoons of the prophet Mohammed. Information was passed to the FBI and he was thereafter, until his arrest that October, kept under targeted US surveillance.

An intelligence expert and former CIA operative, who asked to remain anonymous because he had been directly involved in the Headley case, was derisive about the claim that data-mining sweeps by the NSA were key to the investigation. "That's nonsense. It played no role at all in the Headley case. That's not the way it happened at all," he said.

The intelligence expert said that it was a far more ordinary lead that ensnared Headley. British investigators spotted him when he contacted an informant.

The Headley case is a peculiar choice for the administration to highlight as an example of the virtues of data-mining. The fact that the Mumbai attacks occurred, with such devastating effect, in itself suggests that the NSA's secret programmes were limited in their value as he was captured only after the event.

Headley was also subject to a plethora of more conventionally obtained intelligence that questions the central role claimed for the NSA's data sweeps behind his arrest. In a long profile of Headley, the investigative website ProPublica pointed out that he had been an informant working for the Drug Enforcement Administration perhaps as recently as 2005. There are suggestions that he might have then worked in some capacity for the FBI or CIA.

Headley was also, ProPublica found, the subject of several inquiries by agents of the FBI-led Joint Terrorism Task Force. A year before the Mumbai attacks his then wife, Faiza Outalha, reported on him to the US embassy Islamabad, saying he was on a secret mission in India and was a "drug dealer, terrorist and spy".