The spokesperson said the police is treating the attack as an attempted murder.
The spokesperson also denied that the police had ever commented on one of the attackers leaving behind a mobile phone at the crime scene as it was claimed earlier. He said the inquiry is continuing and the police has appealed to the public for any assistance.
Brar, who received injuries during the attack returned back to Mumbai along with his wife on Wednesday.
Brar, 78, has said that he is convinced it was an attempt to assassinate him by "pro-Khalistan elements" for his role in the 1984 "Operation Bluestar" that was aimed at flushing out Sikh militants led by Jarnail Singh Bhindrawale from the Golden Temple.
After the attack on Sunday night, Brar said he had informed local army authorities about his private visit to London, but the Indian high commission here said it was unaware of his visit.
Brar assailants had 'long beards': Police
Brar assault: Lack of communication to blame?
Gen Brar's lack of security in London needs to be probed
Should our aging national heroes be left to defend themselves?
Lt Gen Brar to be relocated to safer location