Chris Driver-Williams, a former senior IED analyst for the Defence Intelligence Staff said his claim provoked laughter at a meeting of intelligence agencies on the morning of the bombings.
One senior intelligence officer attending the Cobra meeting said the idea of an al Qaeda link was "absurd".
"When I suggested this at Cobra, I was met with laughter. This was by people in the intelligence community who knew their onions," Mr Driver-Williams said.
"Someone senior from an intelligence organisation said: 'Who are you and what possibly qualifies you to come out with such an absurd statement?"'
Later that day the al Qaida link was widely accepted by investigators as the details of the simultaneous planned attacks became clear.
Mr Driver-Williams, an expert in suicide terrorism, said the meeting showed the "information vortex" as the first reports of the blasts came in.
It comes as the Intelligence and Security Committee is due to publish its second report in to the bombings which claimed the lives of 52 people and left hundreds more injured.
It is expected to clear the Security Service of missing opportunities to prevent the attacks.
Victims of the bombings have hit out ahead of the report that they fear will be a "whitewash" and clear MI5 and the police of missing vital opportunities to stop the attacks.
A group of 25 people who were caught up in the attacks and relatives of those who died, have launched a legal battle for a public inquiry amid concerns that a report by MPs due out today will not give them the answers they are looking for.
The parliamentary Intelligence and Security Committee (ISC), appointed by the Prime Minister, is due to issue its second report on the bombings, after the first was accused of ignoring vital questions.
It later emerged that both Sidique Khan and Tanweer had been extensively photographed in 2004 by MI5 and the police as part of Operation Crevice, focused on Omar Khyam and his associates, who were planning a fertiliser bomb attack on the Bluewater Shopping Centre in Kent and the Ministry of Sound nightclub in central London.
The earlier ISC report concluded the decision of the security services not to prioritise Sidique Khan and Tanweer after the arrest of the fertiliser gang was "understandable" but the families think otherwise.
Rachel North, who survived the attacks and represents the 7/7 Inquiry Campaign Group, said: "It is not about who did right or who did wrong, it's about could it have been stopped."
Robert Webb, whose sister Laura died in the attacks, said: "Something has clearly gone wrong, whether it is an error of judgement, lack of resource or break-down in communication, there is a problem and there cannot be any other conclusion than that.
"I think we have just got to keep on the road for an independent review. If there are questions over the death of a loved one you want to try and find out the truth for them."
The families want to know why a number of potential leads were not followed up:
* Sidique Khan's name and telephone number were found in 2003 on the mobile phone of Mohammed Quayam Khan, who allegedly acted as a go-between for both the July 7 attackers and the fertiliser gang.
* MI5 knew Sidique Khan had attended a key meeting which led to the fertiliser bomb plot and considered him important enough to follow him back to his mother-in-law's address in Dewsbury, West Yorkshire on two separate occasions.
* The pair were observed meeting Khyam on four separate occasions between February and March 2004, three of which led to clear surveillance photographs of the men being taken at the Toddington services on the M1, outside a McDonald's in Crawley and walking towards an Islamic bookshop in Upton, east London.
* Had the photographs been shown to Mohammed Junaid Babar, a US supergrass who later spotted Sidique Khan in a newspaper story on the July 7 attacks, he could have told MI5 about a key al-Qaeda training camp the men attended in Pakistan in 2003.
* Police approached a garage that had given Mohammed Sidique Khan a courtesy car which he had used for meetings with the fertiliser gang and was given his correct name, address and telephone number in January 2005, but apparently took the matter no further. An inquiry a few weeks later showed he had insured another car in his own name.
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