Linda Carty, 50, was sentenced to death in 2002 for her part in the abduction and murder of a 25-year-old woman after a trial campaigners say was "catastrophically flawed".
She was due to become the latest person to "appear" on the London monument as part of the long-running Antony Gormley One & Other Exhibition and will use the platform to appeal for help.
A life-size cardboard cut-out of the death row prisoner was due to stand on the platform from 10am to 11am and a recorded message from Carty will also be played calling on the British public and Government to intervene to help save her from the lethal injection.
In the message, Carty states: "Time is now running out and I appeal to every one of you and to the British Government to please help me."
She adds: "I'm sorry if I sound like a desperate woman. I am desperate, because the British people may be my last hope. If they ask for my life to be spared, maybe Texas will listen."
Carty has always maintained her innocence, but with her appeal now in its later stages, her execution could be just months away, supporters fear.
Speaking from her Texas prison, Carty said she was hopeful that her appeal - which is currently lodged with the Fifth Circuit Court of Appeals - would be successful.
But she added that her case needed support from influential people, possibly from outside the US.
"Texas doesn't care about clearing my name. It is going to have to come down to either the British Government, a member of parliament or a US senator," she said.
Asked if she thought the British Government and Prime Minister could assert more pressure, she replied: "He has to. You cannot sit passively by and because you have a good relationship with the US say 'I don't want to rock the boat'. You are talking about somebody's life here."
She added: "He has to get up and say 'I am not going to allow you to kill this lady'."
Clive Stafford Smith, director of legal charity Reprieve, said: "Linda Carty's speech to Trafalgar Square shows that she is a terrified woman, and with good reason. Texas plans to kill her by lethal injection, which is a painful and lonely death.
"The British Government must do everything in its power to prevent Linda's death."
Earlier this year, the Foreign Office did intervene in the legal process, filing an amicus brief to the US Appeals Court complaining of lack of notification of the woman's original arrest in 2001 and "ineffective counsel".
Carty was born on the Caribbean island of St Kitts to parents from the British overseas territory of Anguilla. She holds a UK dependent territory passport.
As such, her arrest should have been notified to the British Embassy under a long-standing agreement. But her state-appointed lawyer did not inform her of her right to seek assistance from the British consulate - one of a catalogue of errors, supporters claim.
A spokeswoman for the Foreign office said earlier this year that it would make representations against the use of the death penalty.
Carty has now been on death row for eight years. She was convicted in connection to the kidnap and murder of Joana Rodriguez, who was seized alongside her four-day-old son by three men on May 16 2001.
The baby was later found unharmed in a car, but Rodriguez was found dead, having suffocated with duct-tape over her mouth and a plastic bag placed around her head.
At the subsequent trial, prosecutors argued that the men were hired by Carty who, unable to get pregnant herself, intended to "cut the baby out" of the woman and pass the child off as her own.
It was claimed that the accused had bought surgical scissors ahead of the abduction.
According to Reprieve, the prosecution's claim should have been objected to on the grounds that the baby had already been born and the inadequacy of the scissors purchased if they were to be used for such a procedure.
It is one of a number of defence failings during the trial, campaigners have claimed.
They note that the court-appointed defence lawyer has seen 20 of his clients end up on death row - believed to be the highest of any defence lawyer in the US.
Carty believes she was framed for the crime by the three men who carried out the abduction due to her earlier work as an informant for the Drug Enforcement Agency (DEA).
From the 1980s onwards, Carty, a former primary school teacher, was employed by the DEA to befriend suspected drug traffickers in order to get information out of them.
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