we've got signatures, help us get to 30,000 by January 22, 2014
Foreign Office minister Hugo Swire said the government objected and that appeal options were open to Lindsay Sandiford.
Sandiford, 56, was arrested at Bali's airport in May 2012 after 4.8kg (10.6lb) of cocaine was found in her suitcase lining during a routine check.
She faces death by firing squad.
Sandiford says she was coerced into carrying drugs by gangsters who were threatening to hurt one of her children.
Mr Swire told the Commons: "We strongly object to the death penalty and continue to provide consular assistance to Lindsay and her family during this difficult time."
He told MPs "repeated representations" had been made to the Indonesian authorities and Foreign Secretary William Hague had raised the case with his counterpart in the country.
"We understand that, under Indonesian law, Lindsay has at least two further avenues of appeal through the courts as well as an opportunity to apply for presidential clemency should these be unsuccessful," he said.
Sandiford's lawyers said they were "surprised" at the verdict and would appeal - prosecutors had recommended a 15-year prison sentence.
But the judges at Denpasar District Court said there were no mitigating circumstances and the defendant did not appear to care about the consequences of her actions.
They said Sandiford had damaged the image of Bali as a tourism destination and weakened the government's anti-drugs programme.
The defendant appeared shocked as the sentence was handed down. She covered her head with a brown sarong to hide her face from the glare of cameras.
Sandiford is originally from Redcar in Teesside but her last UK address was in Gloucestershire.
She was arrested after a flight from Bangkok, Thailand, and accused of being at the centre of a ring involving three other Britons.
Paul Beales was sentenced last year to four years for possession of drugs. Rachel Dougall was jailed for one year for failing to report a crime.
The drug possession trial of Brighton man Julian Ponder - believed to be Dougall's partner - is still taking place. A verdict is expected on Wednesday.
He is alleged to have collected cocaine from Sandiford.
Her case had been taken up by the British human rights charity, Reprieve, which said Sandiford was "targeted by drug traffickers who exploited her vulnerability and made threats against her children".
The charity said she was held for 10 days without access to a lawyer or translator after her arrest and the Indonesian authorities had failed to inform the British embassy during this time.
In response to the sentence, Reprieve's Harriet McCulloch said: "She is clearly not a drug king pin - she has no money to pay for a lawyer, for the travel costs of defence witnesses or even for essentials like food and water.
"She has cooperated fully with the Indonesian authorities but has been sentenced to death while the gang operating in the UK, Thailand and Indonesia remain free to target other vulnerable people."
During the trial Sandiford's defence lawyer said a history of mental health problems made her client vulnerable.
In a witness statement, Mrs Sandiford apologised to "the Republic of Indonesia and the Indonesian people" for her actions.
She added: "I would never have become involved in something like this but the lives of my children were in danger and I felt I had to protect them".
In another statement to court, her son Eliot said he believed his mother was forced into trafficking after a disagreement over rent money she paid on his behalf.
Indonesia has some of the toughest anti-drug laws in the world, but BBC correspondents say executions rarely take place.
Most of the 40 foreigners currently on death row in Indonesia have been convicted of drug offences, according to Australia's Lowy Institute for International Policy.
Five foreigners have been executed since 1998, all for drug crimes, but there have been no executions in the country since 2008, it said.
The UK Foreign Office says there are currently 12 British nationals facing the death penalty abroad. A further 55 face charges which carry a possible death sentence.
BBC political correspondent Norman Smith said any pressure by the UK government in Sandiford's case was likely to occur after the judicial appeals process was complete.
Punishment To Harsh For The Crime
She did not attack anyone or cause any harm; the idea of her being put to death to defend her child is outrageous. We call on the Bali Government to stop the death penelty charges and allow her to carry out a sentence in Britain where her children and grandchildren can visit her regulary.
Lindsay Sandiford is innocent, she did not murder or commit any offence other then drug smuggling.
If everything looks correct, click sign now. Your signature will not be added until you click the button below.