Sunday attack on 78-year-old Brar in Old Quebec Street near Oxford Street were two women.
"Officers from the Counter Terrorism Command have arrested a further eight people in connection with the investigation into the attempted murder of an Indian man (Brar) in central London on 30 September," the Metropolitan Police Service said in a statement.
The statement came as Britain's foreign office minister in charge of India, Hugo Swire, called the attack on Brar "unacceptable" and "appalling", saying it was of "great concern" to the UK.
"It (the attack on Brar) is of great concern to the United Kingdom. We don't want these people here exporting their terrorist views because they represent a real threat to people in the UK apart from anything else.
"It is regarded as being as unacceptable and despicable as people in India do. These things are taken very seriously by this government. General Brar was appallingly, appallingly attacked. It would be wrong for me to comment (further) till we know who the perpetrators are," Swire said.
Apart from the eight arrested today over the attack on Brar, the Scotland Yard said a further three people were held on immigration matters. The three were nabbed at the same address from where some of the suspects were held.
Giving details about today's arrests, police said two people -- a 42-year-old man and a 38-year-old woman -- were arrested at a residential address in Hillingdon borough. The man was held on suspicion of assisting an offender and the woman was arrested on suspicion of conspiracy to murder.
A further three men, aged 42, 37 and 30 respectively, were arrested after a short while on the street on Queensdale Road, in Kensington and Chelsea borough, on suspicion of conspiracy to murder, the statement said.
Three more people were held at a residential address in Holland Park after a few hours. Two of them were arrested on conspiracy to murder while the third one was held on suspicion of assisting an offender.
Another three men, aged 45, 29 and 28 respectively, were arrested at the same address on suspicion of immigration matters.
The arrests came a day after officers took into custody three men and one woman on suspicion of conspiracy to murder in connection with the investigation into the attempted murder of Brar.
"All 15 are in custody at police stations in central London and west London," the Scotland Yard statement said.
A number of search warrants have also been executed in connection with this investigation, it said.
"The searches are being carried out at a residential address in South Shields, a residential address in Birmingham and two residential addresses in London."
"Enquiries are ongoing and police continue to appeal for information about the incident," it said.
The police statement said the detectives from New Scotland Yard are investigating the incident and treating it as an attempted murder.
"They have maintained an open mind regarding the motive for this attack and the investigation will continue to go where the evidence leads."
Brar, who had led Operation Blue Star in 1984 to flush out pro-Khalistan militants from the Golden Temple, was on a private visit here when he was attacked by four men, suspected to be Khalistan sympathisers, while he was returning to his hotel with his wife.
He suffered a wound on his neck and cheek but his wife was not injured in the attack.
The four men who attacked Brar were described as being of Asian appearance, all with long beards, and were wearing dark clothing and long black jackets.