The Saudi Air Force is being trained by the British Government amid accusations that it is carrying out atrocities in neighbouring Yemen, it has emerged.

The Liberal Democrats seized on the instruction being given, in both Saudi Arabia and the UK itself – describing the revelation as “shameful”.

Tom Brake, the party’s foreign affairs spokesman, called on the Ministry of Defence (MoD) to end the training immediately and for much stricter controls on arms exports to the oil-rich kingdom.

Defence Secretary Michael Fallon said the Royal Saudi Air Force was helped in order to “improve their targeting processes” – and, therefore, their compliance with international law.

But Mr Brake said: "It is shameful that the UK Government is not only arming Saudi pilots, it is training them as well. The indiscriminate bombing of innocent civilians by Saudi Arabia in Yemen, in clear breach of international humanitarian law, is now well documented. The Government must end its complicity in this murderous campaign.”

The training opens up a new front in criticism of Britain’s close links with Saudi Arabia – with the Saudis currently leading a coalition bombing campaign against Houthi rebels in Yemen – at growing humanitarian cost.

Earlier this month, air strikes carried out by the coalition’s air forces killed at least 140 people and injured up to 600 more at a funeral. A report by the Saudi-led coalition’s Joint Incidents Assessment Team (JIAT) admitted responsibility having promised an investigation into the incident, but blamed “wrong information” from allies of the internationally recognised Yemeni government, which it is supporting in the conflict.

“A party affiliated to the Yemeni presidency of the general chief of staff wrongly passed information that there was a gathering of armed Houthi leaders in a known location in Sanaa, and insisted that the location be targeted immediately,” investigators said in a statement at the time.

Saudi Arabia insists the coalition it leads keeps to international laws, with any incidents investigated.

Despite the accusations of alleged war crimes, Theresa May has defended selling arms to Saudi Arabia by insisting close ties “keep people on the streets of Britain safe”.

The admission that training is also taking place came in a written parliamentary answer obtained by Labour MP Stephen Doughty from Mr Fallon.

The Liberal Democrat demanded to know what training and advice had been given by the UK on authorising military operations and the “targeting of aerial operations” over the past year.

In reply, Mr Fallon wrote: “As part of our ongoing defence engagement with Saudi Arabia, the UK has provided training to the Royal Saudi Air Force (RSAF) both in the UK and in Saudi Arabia, including international targeting courses for RSAF personnel, to improve their targeting processes and to support International Humanitarian Law (IHL) compliance.”

The Defence Secretary said the UK had also delivered two training sessions in Saudi Arabia on the process for investigating alleged IHL violations, under a joint incident team it supported.

But he added: “The UK has not been directly involved in investigations undertaken by the JIAT, has not provided any specific operational advice to the Kingdom of Saudi Arabia for operations in Yemen and has not provided training on political authorisation of military operations.”

Saudi Arabia has insisted its campaign in Yemen is being waged "in accordance with international humanitarian law, in a legitimate war of self defence, in a legitimate war to defend the legitimate government of Yemen".

Mr Brake said the latest revelation emphasised the urgent need for strict rules to require the Foreign Secretary to sign off personally any arms sales to countries such as Saudi Arabia.

His plan would see all 28 countries on the Foreign Office’s "countries of concern" list – which also includes China and Russia – denied arms without proof there was “no risk they’ll be used in human rights abuses”.