Five opposition parties in Westminster have called on the UK to end arms sales to Saudi Arabia on the fourth anniversary of the Yemen civil war, saying it has contributed to a catastrophic humanitarian crisis.

The letter signed by leaders of the Labour party, Scottish National party, Liberal Democrats, Plaid Cymru and the Green party, comes as a fragile truce negotiated in December hangs by a thread.

The UN special envoy for Yemen, Martin Griffiths, is due in London this week to discuss his efforts to enforce outline agreements on a redeployment of forces in Hodeidah, the strategic Red Sea port that lies at the heart of the conflict between the Saudi-backed Yemen government and the Iran-supported Houthi rebels.

The Houthis control Hodeidah, the capital Sana’a and the north of the country.

Griffiths has been unable to persuade both sides to agree on the composition of a new civilian force to police Hodeidah, the first step in what is intended as a redeployment of Houthi forces away from the city and the port. Aid workers from Hodeidah say the city’s public services have effectively collapsed.

In their joint letter to the foreign secretary, Jeremy Hunt, the opposition leaders, including the SNP leader in the Commons – Ian Blackford, Labour leader Jeremy Corbyn and the Lib Dem leader Vince Cable, say it is shameful the UK government has not used all means at its disposal to put pressure on Saudi Arabia “to abide by basic human rights laws”. It said Germany, Spain, Denmark, Canada, the US Congress, the UN human rights council and the European parliament have all called for a suspension of arms sales on this basis.

“It is morally reprehensible that the UK government is not only not considering changing its policy, but is actively lobbying other foreign governments, as it did with Germany, to resume arms sales to Saudi,” the letter said.

The authors describe Saudi behaviour in Yemen as reckless and barbaric, saying all arms sales for use in the country should be suspended pending an independent investigation into Saudi conduct in the war.

They add that despite British claims of leverage over Riyadh, there is no evidence that Saudi behaviour has been restrained.

“The UK government is on the wrong side of history,” Blackford said. “This cross-party letter must serve as a wake up call for the foreign secretary that the UK government must urgently recognise the devastating reality of the war in Yemen, get its act together and bring this conflict to an end.”

The Saudis and the United Arab Emirates are meanwhile putting pressure on the UN to declare that the Houthis have failed to comply with agreements reached in Stockholm, so in effect declaring the outline deal is dead. Such a move would lead to the UAE forces restarting their attack on Hodeidah.

Michelle Bachelet, the United Nations high commissioner for human rights, warned that children in Yemen continued to be killed and maimed at an alarming rate, despite the three-month-old truce in Hodeidah.

“Since the Stockholm agreement on 13 December, it is estimated that eight children have been killed or injured in Yemen every day,” Bachelet told the UN human rights council on Wednesday.