Australian immigration minister Kevin Andrews, who is under fire for his decision to cancel Indian doctor Mohammed Haneef's visa, Monday refused to release "the information" on which basis he arrived at the decision.

Andrews told ABC radio this morning said the information may not be released after discussions with the Australian Federal Police Commissioner Mick Keelty.

"One of the difficulties in this regard is that there is an ongoing investigation both in Australia and in the UK, and the Commissioner of the AFP Keelty has said to me that this protected material, if released, could jeopardise that investigation," he said.

"I think I have a responsibility not to jeopardise an investigation in this manner," he said.

The minister said he wanted to release to the public extra information which he said led him to cancel Haneef's visa on character grounds.

Andrews and the Australian Federal Police had indicated the decision to cancel the visa had been made on basis of information not provided to the court.

Prominent lawyer Lex Lasry said police may not want Andrews to release the secret information because of embarrassment about its lack of substance.

Lasry, chairman of the Victorian Criminal Bar Association and a high-profile human rights advocate, Tuesday said there were two reasons why police may want to keep the information under wraps.

"One is the police are embarrassed about the lack of substance to the information and would find it embarrassing if it was released," Lasry told ABC radio.

"The alternative version is that there is some continuing investigation and that they don't want that investigation prejudiced," Lasry further said.

"In either case, but particularly in the second case, that puts the minister, I would have thought, in a fairly difficult position," he added.

Asked whether he has sympathy for Andrews, Lasry said "No I don't because I thought at the time that the visa was cancelled that it looked very much like a misuse of his power.      "I suppose we have to wait and see what the factual basis for that decision was. But at the moment it still looks like a misuse of power to me," he said.

Meanwhile, ABC reported that United Kingdom police have not rejected suggestions there may have been wrong information passed onto Australian authorities, particularly a mobile telephone SIM card.

A Commonwealth prosecutor Clive Porritt mistakenly told the Queensland magistrates court the card was in Glasgow at the time a relative of Haneef rammed a car into an airport terminal. It was actually in Liverpool.

However, the AFP have maintained its investigators knew the card was in Liverpool and the error was a mistake in court not in its briefings.