David Cameron has boasted of his efforts to help sell “brilliant things” such as Eurofighter Typhoons to Saudi Arabia on the day the European parliament voted for an arms embargo on the country over its bombardment of Yemen.

The prime minister talked of the UK government’s role in selling equipment made by defence company BAE Systems to Saudi Arabia, Oman and other countries as he visited the firm’s factory in Preston.

At almost the same time, the European parliament voted in favour of an EU-wide ban on arms being sold to Saudi Arabia in protest at its heavy aerial bombing of Yemen, which has been condemned by the UN. The vote does not force EU member states to comply but it increases pressure on national governments to re-examine their relationships with Riyadh.

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The UK government has been providing training to Saudi forces on how to comply with international law as they identify targets for bombing. It has also been participating in efforts to sell the Eurofighter Typhoon military planes to Saudi Arabia, which has spent £3bn on UK aircraft, arms and other military kit in the last year alone.

There were signs last year that the Eurofighter deal might have been called off over a diplomatic cooling after Michael Gove, the justice secretary, dropped plans for a contract to provide training in Saudi prisons over human rights concerns. The deal now appears to be progressing again.

Asked by an employee how he was helping boost exports of the Eurofighter, Cameron said: “With the Typhoon there is an alliance of countries: the Italians, Germans and ourselves. We spend a lot of time trying to work out who is best placed to win these export orders. We’ve got hopefully good news coming from Kuwait. The Italians have been doing a lot of work there. The British have been working very hard in Oman.

Oman’s Sayyid Fahd bin Mahmoud al-Said greets David Cameron in December 2012 after his arrival in Muscat following a BAE Systems deal to sell planes to the country. Photograph: AFP/Getty Images

“I can see the planes being built right behind me here. We’ve got more work to do in Saudi Arabia. The Germans have done a lot of work as well. It is a collaborative project. We use the collective skills but also the collaborative muscles of all the governments to try and help make sure we can sell them around the world.”

He then gave a further reassurance to BAE that he would not let the EU referendum distract him from helping sell its products across the world. “I’m going to be spending a lot of the next four months talking about this issue but I promise I will not be taking my eye off the ball, making sure the brilliant things you make here at BAE Systems are available and sold all over the world. We have some of the toughest rules on defence exports – and rightly so – but I think it is absolutely right to get behind companies like this … to safeguard jobs and and skills and investment by making sure we can sell these things around the world.”

The Labour party leader, Jeremy Corbyn, has been extremely critical of Cameron’s relationship with Saudi Arabia because of its human rights record, prompting an angry response from Riyadh.

Hilary Benn, the shadow foreign secretary, has also called for an immediate review of arms exports licences over the situation in Yemen, saying it looks like international law has been breached.

Oliver Sprague, Amnesty International UK’s arms controls director, said: “The ‘brilliant things’ that David Cameron says BAE sells include massive amounts of weaponry for the Saudi Arabia military, despite Saudi Arabia’s dreadful record in Yemen.

“Thousands of Yemeni civilians have been killed and injured in devastating and indiscriminate Saudi coalition airstrikes, and there’s strong evidence that further weapons sales to Saudi Arabia are not just ill-advised but actually illegal.

“Mr Cameron should stop acting as a cheerleader for BAE’s reckless arms sales and stop the flow of weapons to the Saudi war machine pending the outcome of both a UN inquiry into the bloody conflict in Yemen and the UK’s own review of its arms exports to Saudi Arabia.”