Some 199 Britons are "highly likely" to have died in the tsunami that has killed at least 144,000 people, Jack Straw has said.
Most of the British deaths have been in Thailand
The foreign secretary said 159 Britons were missing and feared killed, in addition to 40 already confirmed dead.
Because "many of the bodies of the dead may sadly never be found, firm estimates of casualty figures remain difficult", Mr Straw added.
Prime Minister Tony Blair has returned to the UK after being on holiday.
Liberal Democrat leader Charles Kennedy and Tory leader Michael Howard had suggested the prime minister should have returned early from his Egyptian vacation following the tsunami.
Most of the British deaths had been in Thailand, where 43 UK police officers were now involved in the search for missing Britons, Mr Straw said.
Rejecting criticism over the prime minister's absence, the foreign secretary said: "Is there a single thing the British government could and should have done that it has not done, notwithstanding the fact the prime minister is abroad? The answer is 'no'."
He added: "There is no cap on the amount of money that can be made available by the British government.
"The crucial issue is to ensure that it is spent as quickly as possible."
The government was contributing money towards the cost of travelling to South East Asia for victims' relatives, and towards the repatriation of remains, Mr Straw said.
He added that the police had appointed 113 family liaison officers to counsel relatives.
Mr Straw said he would be making a personal donation towards the relief effort.
Emergency supplies from Britain have begun reaching the disaster region, where 1.8 million people need food aid and an estimated five million have been made homeless.
FOREIGN TSUNAMI VICTIMS
Germany: 60 dead
Sweden: 52 dead
Britain: 40 dead
France: 22 dead
Up to 560 missing
Norway: 21 dead
Japan: 21 dead
Italy: 18 dead
Switzerland: 16 dead
US: 15 dead
Australia: 12 dead
South Korea: 11 dead
Final figures expected to rise.
Sources: Reuters, AP
Three RAF flights, in a joint operation between the UK's Department for International Development (DFID), Finland, Sweden, Denmark and Norway, are delivering to Indonesia supplies including one million water purification tablets.
UK charities have also begun chartering planes to deliver aid to the region. "The money being raised is being put to work now," said Disasters Emergency Committee spokeswoman Jane Moyo.
The government has sent two ships - the Royal Fleet Auxiliary ship Diligence and frigate HMS Chatham - to the disaster area.
It has also announced that a second Royal Fleet Auxiliary vessel, the Bayleaf, is being sent.
The Ministry of Defence is also sending a reconnaissance team to Indonesia's Aceh province to assess what help the UK military might be able to give.
Similar squads have already been deployed to Colombo, in Sri Lanka, and Jakarta, the Indonesian capital.