The lack of workers in slaughterhouses and supply chain disruption has led to a swelling backlog of pigs on farms.
Around 120,000 are expected to be shot with a captive bolt and the carcasses disposed of rather than going into the food chain. The National Pig Association says culling has started on a handful of farms.
Boris Johnson dismissed concerns about animal welfare, saying the pigs were going to die anyway.
But the RSPCA urged the government to take immediate action “to safeguard the welfare of animals and support British farmers”.
Slaughterhouses are specifically designed to kill animals, the charity said, and shooting thousands of healthy pigs on a farm “will be extremely difficult, even for a skilled expert”.
However, animal-welfare experts at Compassion in World Farming said shooting was greatly preferable to a slaughterhouse death, where most are poisoned with high concentrations of carbon dioxide gas, causing immense suffering and an “inhumane” death.
“CO2 causes ‘severe respiratory distress’ – in the words of a scientific paper,” said chief policy adviser Peter Stevenson.
“The pigs can be seen hyperventilating, struggling for breath and trying to escape from the gas chamber.”
Mr Stevenson told The Independent: “I definitely disagree with the RSPCA. I’m not suggesting on-farm slaughter is good, but the use of high levels of CO2 causes immense suffering. It makes a mockery of the term ‘humane slaughter’.”
Emma Slawinski, of the RSPCA, which has previously lobbied against use of carbon dioxide, said: “Slaughterhouses are specifically designed to kill animals. Shooting thousands of healthy pigs on a farm will be extremely difficult, even for a skilled expert.
“Pigs are intelligent, big and strong animals, weighing as much as an adult man, and getting a clean shot will be difficult, even for a skilled expert.
“Farmers want to do the right thing and get their animals to slaughterhouses where they can be slaughtered more humanely.”
Mr Stevenson agreed stunning pigs with a captive bolt was not easy, but said if carried out correctly it would produce instant unconsciousness, which was “greatly preferable” to carbon dioxide.
Alternative methods include lethal injection and electrical stunning. He said: “If done correctly, this would produce instant unconsciousness.
“For me, the debate is not about slaughter on farm or in a slaughterhouse, but exposing the fact that normal slaughter for pigs is horrendous in the vast majority of cases. This element is missing from the current debate on the plight of the pig sector.”
In 2003 the Farm Animal Welfare Council advised phasing out the use of carbon dioxide within five years. But instead, Mr Stevenson said, use of the “inhumane” practice was on the increase.
An RSPCA spokeswoman said the charity wanted CO2 banned and humane alternatives to be developed urgently.
In 2018, it wrote a joint letter with CiWF to the government, calling for a ban by 2024.
A leading supplier of pig meat says the labour shortage means cheap EU pork imports are flooding the UK market, undercutting British farmers.
The industry is short of 15,000 workers, according to the British Meat Processors Association.