SOURCEVilasrao Deshmukh, the chief minister of Mumbai, was reported to have said that two British-born Pakistanis were among eight gunmen seized by Indian commandos who stormed buildings to free hostages.
The Foreign Office said it was investigating reports on NDTV, a local television news channel, that the terrorists – who swarmed into luxury hotels and other tourist sites in the city – included "British citizens of Pakistani origin".
Jacqui Smith, the Home Secretary, said the Government had "no knowledge" of any British suspects.
"We will do anything we can to help Indian authorities through what is obviously a very difficult time," Miss Smith said. "We will do what is necessary. At the moment the priority is to support the immediate needs.
Earlier on Friday, Gordon Brown said he "would not want to be drawn into early conclusions" over the claims.
The Prime Minister called for international co-ordination to combat terrorism in the wake of the attacks, which he called "atrocious". He said: "We have got to look at how international action against terrorism can be improved."
"Obviously when you have terrorists operating in one country, they may be getting support from another country or coming from another country, and it is very important that we strengthen the co-operation between India and Britain in dealing with these instances of terrorist attacks," he told Sky News.
The Prime Minister's comments came as Indian commando troops cleared the last terrorists from buildings across Mumbai.
The troops killed at least two militants at the Trident Oberoi hotel, where police found 24 bodies. About 93 guests and staff – including two Britons and another clutching a baby – were rushed out and loaded into waiting cars, buses and ambulances.
JK Dutt, the director general of India's National Security Guard, said the hotel had been brought "under our control".
"We have killed two terrorists today," he said. "There was lots of firing, they also lobbed hand grenades. Some of them are unexploded, we are going to defuse them – you may hear some sound of explosions."
It is thought that more than 100 commandos entered the Taj Mahal hotel – in which a hostage situation was thought to have ended on Thursday – and gunfire and explosions have been heard. Police reported finding at least 30 bodies in one hall of the hotel.
Troops also stormed the Nariman House complex in the south of the city, which houses a Jewish group. A woman and a child were seen leaving the building after the commandos, who arrived in helicopters, abseiled down ropes to secure the building.
Mr Brown, who is to talk to Indian Prime Minister Manmohan Singh later on Friday, said he did not believe there were any further Britons among the hostages.
One Briton, Andreas Liveras, the founder of a luxury yacht business who was in his 70s, has been confirmed among the dead, while at least seven are known to have been injured.
Mr Brown said: "Of course, we are mourning the death of a British citizen who has died and as the high commissioner visits hospitals in the Mumbai area, we are hoping to discover more in terms of the number of people injured."
Mark Abell, a British lawyer, who on Thursday spoke to The Daily Telegraph while barricaded into his hotel room at the Oberoi, was among those released. He said: "I'm going home, I'm going to see my wife."
He added: "These people here have been fantastic, the Indian authorities, the hotel staff. I think they are a great advertisement for their country."
Another man, who said he was British but would not give his name, said: "I didn't see anything. I just heard loud blasts. I was in my room. I didn't get out until an hour ago."
Nicole Griffen, another Briton, said she had been rescued by Indian special forces from the Taj Mahal.
She told BBC Radio 5 Live: "They entered and looked through our passports and scouted around to see if there was (anyone) harbouring terrorists or attackers.
"And then we were promptly told where to go by the central stairway and again we were asked to wait with other guests while they checked other floors and checked other rooms and we all congregated into one space where they could protect us centrally."
A group calling itself Deccan Mujahideen has claimed responsibility for the attacks. However, Mr Singh blamed "external forces" for the violence - a phrase sometimes used to refer to Pakistani militants, whom Indian authorities often blame for attacks."
Pranab Mukherjee, the country's foreign minister, was more explicit. "According to preliminary information, some elements in Pakistan are responsible," he said.
I can say a thousand things right now, but choose to keep my mouth shut. :taped: