Geronimo the alpaca has been sentenced to death after his owner lost a last-ditch High Court bid to save him.
The animal has twice tested positive for bovine tuberculosis.
The Department for Environment, Food and Rural Affairs (Defra) has ordered the destruction of the animal.
His owner Helen Macdonald, who imported him from New Zealand, believes the tests are returning false positives but she has been refused permission to have him tested a third time.
Earlier this month, she lost her final appeal to save her beloved pet at the High Court in London and a warrant was signed for his destruction.
Ms Macdonald, who owns a farm at Wickwar, South Gloucestershire, has received an outpouring of support from the public.
More than 130,000 people signing a petition calling on Boris Johnson to halt the killing.
On Tuesday, an urgent application for a temporary injunction to halt the enforcement of the destruction order was considered by Mrs Justice Stacey at the High Court in London.
However, the judge said she would need further information from Ms Macdonald and from Government lawyers before she could make her decision.
At court on Wednesday, the judge refused the urgent application and concluded there was “no prospect” of Ms Macdonald succeeding in her bid to reopen a previous ruling.
Ned Westaway, representing the Defra executive agency the Animal and Plant Health Agency (Apha), told the court the agency will not seek to execute the warrant on Wednesday evening.
Macdonald would be given the opportunity to make her own arrangements for Geronimo’s destruction.
Her lawyers told the court Geronimo first tested positive for bovine tuberculosis in September 2017 and has been in isolation since.
Catrin McGahey QC told the court although Defra argued in previous hearings that there was a “residual risk” to other animals, the agency has also agreed Ms Macdonald’s bio-security arrangements are “impeccable”.
She said it had come to light following the publicity resulting from Ms Macdonald’s case that other animals who have been subjected to the same testing regime as Geronimo have later showed no signs of the disease after being euthanised.
Ms McGahey said: “The only issue is whether the defendants should have disclosed the fact that they had in their possession evidence that other camelids who had been subjected to repeated priming had gone on to test positive in Enferplex tests, and that there had been no sign of bovine tuberculosis on post-mortem examination.”