Rishi Sunak has promised to ban live animal exports as well as imports of hunting trophies.
In a move that delighted animal-welfare campaigners, the contender to be the next Tory leader and prime minister pledged to champion the Kept Animals Bill, which had appeared doomed under Boris Johnson.
His decision puts pressure on rival Liz Truss to follow suit – although her record on animal welfare is considered unfavourable.
It would also create a new criminal offence of pet abduction.
But the legislation had stalled, prompting widespread fears that it would never be passed.
Thousands of calves and sheep are exported by sea and road from the UK on arduous journeys as far as Spain, Italy and even north Africa, often in extreme temperatures and insufficient food or water.
Meanwhile, the Animals Abroad Bill, which included a ban on importing body parts from hunted wild animals, was dropped at the insistence of Jacob Rees-Mogg and Mark Spencer.
The heads of nearly 30 campaign organisations on Friday wrote to the two leadership candidates calling on them to promise to uphold the pledges in last year’s Conservative Party animal welfare action plan.
Most of the pledges were also in the party’s election manifesto.
Their campaign won the backing of Larry the Downing Street cat, who tweeted: “To my next lodger, please confirm that you will take action for animals.”
Within hours, Mr Sunak’s team replied saying: “Rishi looks forward to championing this Bill as it continues to progress through Parliament,” adding that he was “committed to banning the import of hunting trophies from thousands of species”.
Nick Palmer, Head of Compassion in World Farming UK, said he and the other charity leaders were very disappointed not to have had a reply from Ms Truss.
“We all felt up to now that neither candidate was showing a great deal of interest in animal welfare so we feel this is a very positive move.”
The Independent has contacted Ms Truss’s team.