Pressure within government ranks for a ban on the live sheep trade to the Middle East has increased, with a second Liberal MP calling for the exports to end.

Jason Wood, who holds the outer Melbourne seat of La Trobe, said on Wednesday that even if standards were toughened the trade would remain inhumane.

Wood’s call follows NSW Liberal and former health minister Sussan Ley declaring the trade should cease.

Ley, from the regional electorate of Farrer, last week wrote to Agriculture Minister David Littleproud saying that: “In the face of what is rapidly becoming a national shame, it is my view that Australians have crossed a line on this issue. The goodwill that many of us had for the industry is gone. It will not return. The wave of revulsion we are all witnessing will not subside until we, as a nation take the necessary next steps.”

Wood, who chairs the parliamentary RSPCA friendship group, said he had been against the live export trade throughout his career, although up to now he hadn’t called for a ban.

He said that previously, public awareness of the extent of the cruelty probably hadn’t been there, but after the recent 60 Minutes reports the issue had “gone mainstream”. His office had received well over 1000 contacts, of which some 300 had been generated by individuals rather than animal rights groups.

His local Liberal branch members had been shocked and horrified by the latest revelations and they were glad he was taking a stand, Wood said.

He said if there was enough public pressure the politicians “will realise the tide has completely turned”.

Victorian crossbench senator Derryn Hinch, a long-time campaigner against live exports, tweeted on Wednesday: “Our petition calling for Parliament to phase out live exports from Australia over 3 years now near 85,000 signatures. Maintain the rage. I want 100,000 by May 5.”

Littleproud has set up a review of the trade during the northern summer, but so far he has been focused on tightening conditions and oversight rather than ending the exports.

Announcing the terms of reference, Littleproud said this week: “The review will consider stocking density on ships, bedding and animal waste management, ventilation and heat stress risk. It will also consider and evaluate the potential use of air conditioners, and conditions placed on recent voyages, which includes the independent observer paid [and] employed by the Department of Agriculture.”

He said the review would identify “any improvements in how the current standards … can be administered or executed.”

Wood praised Littleproud for “calling the export trade out”, but said that even with improved standards it would be inhumane.

The trade is worth about A$250 million annually, and is particularly centred in Western Australia.

Michelle Grattan does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.