Witnesses told of devastation inside the Taj Mahal Hotel.
A top Indian official has said there was "no authentic information" to suggest that any British citizens were involved in the Mumbai attacks.
Maharashtra state chief minister Vilasrao Deshmukh said he "totally denied" reports.
Gordon Brown said he had spoken to India's prime minister, who "at no point" suggested there was evidence of any terrorist of British origins.
Officials revised the death toll down from 195 to 174 - including one Briton.
A further 239 people were hurt, they said.
There are believed to have been 10 militants involved in the attacks.
Indian officials said their backgrounds were unclear but that the sole surviving gunman was from Pakistan.
Pakistan said it would take action against any group from within its borders if it was involved in "ghastly acts".
Guests who had been holed up during a three-day siege at the Taj Mahal Hotel have been speaking about their ordeal.
Briton Richard Farah, who was trapped in his room before being rescued by commando troops, told how he hid his passport in his false leg after terrorists were reported to be seeking British and American passport holders.
I saw all the blood and broken glass and shrapnel... tonnes of blood and shoes, people's shoes, women's shoes, men's shoes
Mr Farah, who lives in Jamaica but has family in London, told Sky News he saw trails of blood, broken glass and shoes as he was led from the building.
"In the last few hours there were so many explosions and the floors shook. I said 'I'm a goner' because it was right below me."
"Eventually we got to the lobby. I saw all the blood and broken glass and shrapnel... tonnes of blood and shoes, people's shoes, women's shoes, men's shoes."
He added: "I had hidden my passport in my leg, in the lining of the leg. If they had come to get me they wouldn't have found a passport."
Another Briton, Asian actor Joey Jeetun, said that a gun was held to his head after he was rescued from the Leopold Cafe Bar - another of the militants' targets.
He said he was treated as suspicious because he did not look like a Mumbai local and was taken to a police station before being released.
And Welsh couple Lynne and Ken Shaw have told how they escaped through the kitchens of a Chinese restaurant in the Taj Mahal hotel after gunfire started.
They spent several hours in a back room of the hotel before being freed by Indian police.
"It wasn't until they gave me a glass of champagne about 20 minutes into the flight (home) that... I wept because I knew how lucky we had been to get out," said Mrs Shaw of Penarth, Vale of Glamorgan.
The body of the only known British victim, Andreas Liveras, 73, has been flown back to London.
Mr Liveras, a businessman of Cypriot origin, was caught up in the early stages of the Mumbai attacks after he left a yacht moored in the harbour to go ashore for dinner.
At least seven Britons were injured in the attacks on the Indian city.
Vicki Treadell, British Deputy High Commissioner in Mumbai, said she could not rule out more British fatalities and said she had visited "a number" of British nationals in hospital.
Funeral ceremonies have been taking place after the attacks
"They are in remarkably good spirits considering everything they have gone through."
She added that the embassy had helped about 90 people return to Britain and was looking to trace others.
"We are working very closely with the management of all three hotels affected and we will be comparing lists of people we know that relatives are looking for."
Prime Minister Gordon Brown told the think-tank Progress conference in central London on Saturday that he had spoken to his Indian counterpart Manmohan Singh.
"A great multi-faith democracy has been laid low by terrorists," said Mr Brown.
"It raises huge questions about how the world addresses violent extremism."
The Indian community in Britain has been holding prayer services to remember the victims of the attacks in Mumbai.
A series of services were held at the country's biggest Hindu temple, at Neasden in north London.
A spokesman for the temple, Kamlesh Patel, told BBC News the events in Mumbai had caused "deep sorrow and sadness".
"We're certainly getting a lot of expressions of grief and we ourselves see this as our responsibility to bring the community together in praying for the sad victims of this terrible tragedy," he said.
Worshippers at Neasden's temple talk on the impact of the attacks in Mumbai
The England cricket team has returned home after their two remaining one-day internationals against India were cancelled.
The England and Wales Cricket Board said it was now assessing whether it would be "safe and secure" to return to play two Test matches that are scheduled.
Many British people caught up in the attacks are returning on flights to the UK.
Those arriving at Heathrow are being met by police officers, who are also handing out flyers appealing for information.
A team of detectives from Scotland Yard is also flying to Mumbai to help Indian authorities with the investigation.
The Foreign Office has issued an emergency number for people with relatives in Mumbai: 0207 008 0000.
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