Asked if she thought Prime Minister Gordon Brown could assert more pressure, she said: "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. 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."
Carty was convicted in connection to the kidnap and murder of Joana Rodriguez, who was seized with her four-day-old son by three men on 16 May 2001.
But she says she was framed by three men in revenge for her work as an informant with a Drug Enforcement Agency.
Campaigners claim there were a number of defence failings during the trial.
The Foreign Office said that it had made its "usual representations" against the death penalty and that it had registered a complaint with the US Appeals Court about not being informed when Me Carty was first arrested.
A Foreign Office statement said: "We are resolutely opposed to the use of the death penalty.
"Our prime concern is to avoid the execution of British nationals.
"We have made a number of representations to the US Government, on this case and others, concerning our view on the death penalty. The US are fully aware of HMG's stance on the death penalty."
A spokesman for the British Consulate-General in Houston said the consulate remained in "close contact" with Carty and her legal representation in the US and UK, and would continue to provide Carty with consular assistance.
Carty has British dependent territory citizenship because she was born on the island of St Kitts, in the Caribbean, to Anguillan parents.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.