The Australian Immigration Department has given tourist visa to a family member of Indian doctor Mohammed Haneef to provide him support during legal proceedings.

A statement from Immigration Minister Kevin Andrews said Haneef's cousin Imran Siddiqqi has been granted a visa after character and security assessments.

Haneef is charged with recklessly providing support to a terrorist organisation in the failed car bomb plot in the United Kingdom.

He is being held in a Brisbane jail and has had his work visa cancelled.

Meanwhile, the Greens party has joined calls for Andrews to reinstate Haneef's visa, after the release of new information about his alleged link to the UK terrorism plot.

The ABC has been told that Haneef's mobile phone SIM card was not in the jeep that exploded at Glasgow Airport but was found 350 kilometres away at a house in Liverpool.

Greens Senator Kerry Nettle said the Federal government's case against Haneef is falling apart.

"Either it is a massive mistake on the part of the Federal Police and the Australian government or it is them desperately looking to charge Haneef and skimming over the facts of the case in making the decision to charge Haneef," she said.

But Andrews has ruled out reviewing his decision to cancel Haneef's visa on character grounds, despite the new information revealed on Friday.

Haneef's spokesperson said nothing that has been reported in the media alters his decision to cancel the visa.

She said the visa decision was based on a broader range of information than was provided to the magistrate in the bail hearing.

A leading criminal barrister on Friday said an apparent prosecution 'mess-up' meant Haneef was unlikely to be convicted of providing support to a terrorist organisation.

In Haneef's bail application on Saturday, Commonwealth Prosecutor Clive Porritt alleged the Gold Coast-based doctor had given his mobile phone SIM card to his cousin Sabeel Ahmed when he left the UK last July.

He alleged Sabeel had then passed the card on to his brother Kafeel, the driver of a jeep used in a terrorist attack on Glasgow Airport on June 30, and that the card had been found on the wreckage.

However, reports from Britain reveal the SIM card in fact may have been with Sabeel Ahmed in Liverpool at the time of the incident.

Melbourne barrister Peter Faris on Friday said the apparent error in the prosecution's case put before the court had been 'a shocking mess-up.'

'You can't get something that's so central so wrong,' he told ABC radio.

'I think this is fast approaching the situation where there is not a reasonable prospect of a conviction, unless there is some other evidence that we do not know about,' he said, adding, 'I just have trouble seeing a jury convict him on this sort of evidence.'