But the parliamentary move has been condemned as counter-productive by several African countries
Animal trophies, many from hunts in southern Africa, are brought into the UK each year.
Plans for a ban on the import of animal hunting trophies will return to the Commons later.
This is the third attempt to get such imports outlawed, following a Tory manifesto commitment in 2019.But critics say UK MPs should not interfere, as paid-for hunting finances efforts to combat poaching.
Up to 25,000 animal parts have been brought into the UK as hunting trophies since the 1980s, according to the database of the Convention on International Trade in Endangered Species.
The all-party parliamentary group for banning trophy hunting says the CITES figures show numbers have been "Increasing steadily" and include about 5,000 endangered species.
The government first brought forward a ban as part of its Animals Abroad Bill in 2021, but ditched it in May 2022.Conservative MP Henry Smith then put forward his Hunting Trophies private members' bill with government backing, but that also failed last November when it ran out of time in the House of Lords.
Now Labour MP John Spellar has sponsored the legislation as a second private members' bill.
The High Commissioners of six African nations are opposing a UK ban on imports, because they say paid-for hunting funds their anti-poaching efforts.
Mr Spellar told the BBC the law was "well overdue" and he believed had enough support to become law.
Pregnant alpaca killed during New Year's Day hunt.