The foreign office minister Mark Field has promised to get to the bottom of “very serious and well sourced” allegations that British SAS soldiers have been injured in a firefight with Houthi rebel soldiers in Yemen.

He was answering an urgent question asked in the Commons on Tuesday by the shadow foreign secretary, Emily Thornberry, who suggested the Britons may have been witnesses to war crimes, if weekend allegations were true that UK special forces were training child soldiers in the Saudi-led coalition.

She claimed as many as 40% of the soldiers in the Saudi coalition were children, a breach of international humanitarian law.

Field said he would be making inquiries with the Ministry of Defence in light of the report. He was representing the government in the absence of Alistair Burt, who resigned as a Foreign Office minister on Monday night to vote against the government on the Brexit indicative votes amendment.

The UK government has a general policy of not discussing the operations of its special forces but Field seemed determined to provide an explanation to MPs.

The former international development secretary Andrew Mitchell said the allegations were so serious because they flew in the face of successive assurances given by ministers at the despatch box that the UK was not a participant in the civil war in Yemen, and was only providing general logistical support to the Saudis in Riyadh.

There had been social media reports from Yemen in February suggesting that British soldiers had been injured in a firefight, and the Daily Express claimed two SAS members had been injured during a humanitarian operation.

However it was claimed in the Mail on Sunday that Special Boat Squadron were not just involved in humanitarian operations, but providing mentoring teams inside Yemen including medics, translators and forward air controllers whose job is to request air support from the Saudis. It claimed five special forces soldiers have been injured.

Mitchell told the Commons: “These serious allegations that are authoritative and credible, and fly in the face of assurances that have been given from the despatch box on countless occasions.” He said he had tabled a serious written questions on the issue.

Field said he did not want to give inadvertent reassurances that turned out not to be correct.

The claims are politically difficult since ministers are eager to suggest that as the penholder on the Yemen issue at the United Nations, Britain is an honest broker in the civil war, which is now entering its fifth year since the Saudi air campaign started. The UK is known to be close to the Saudi military but denies it is involved in operations against the Houthis in Yemen.

The claims came as the UN special envoy for Yemen, Martin Griffiths, a former British diplomat, travelled to Saudi Arabia in a further effort to break the logjam over talks that are meant to lead to a redeployment of Houthi forces around the Red Sea port and city of Hodeida. He was due to speak to the UK foreign secretary, Jeremy Hunt, to discuss if the Saudis would be willing to put further pressure on the Yemen government to make concessions over the deadlocked talks.

The introduction of a new security force, agreed in outline at the Stockholm peace talks in December, remains stalled over differences about its nature and who would have political control of it.