The Serious Fraud Office was told it would not be able to persuade Saudi Arabia to withdraw a threat to cease co-operation with the UK on counter-terrorism just weeks before it abandoned a high-profile corruption probe into arms deals between the two countries.

Evidence submitted to the House of Lords on Monday reveals Britain’s ambassador to Saudi Arabia warned senior SFO officials – including Robert Wardle, the agency’s former head – that the Saudis did not understand the fraud office was independent of government.

The documents were filed as part of the SFO’s appeal against a damning High Court judgment that it caved in to Saudi threats by scrapping its investigation into the £43bn ($85bn) Al-Yamamah arms deal between Riyadh and BAE Systems, the UK’s largest defence contractor.

The unusual decision to submit new evidence – as well as the SFO’s engagement of Jonathan Sumption QC, a top barrister – shows how critical the case has become for the agency, which has been under near-constant attack since the probe was dropped in December 2006.

The High Court found in April that the SFO ignored the law in apparently bowing to Saudi pressure, in one of the most strongly worded rulings issued by the senior judiciary.

Mr Sumption on Monday told a panel of five law lords that the decision was riddled with errors of fact and law and should be overturned.

The new evidence – submitted in the form of three separate witness statements – focuses on the issue of whether the SFO had taken any steps to rebuff the threats by the Saudi government to withdraw security co-operation.

According to a statement drafted by Helen Garlick, assistant director of the SFO at the time, she and Mr Wardle were advised in late November or early December 2006 – shortly before the investigation was abandoned – that any such approach would not be “viable’’.

Ms Garlick, who recently left the SFO, said they were told by the ambassador that: “The Saudis had a very different understanding of criminal justice systems and despite a great deal of experience in dealing with the West, the Saudis would find it difficult to accept, in comparison with their own system, that the UK government and the prime minister could not stop the investigation if they chose to do so.’’

The hearing continues on Wednesday, with a judgment expected in the autumn. The SFO has always denied any wrongdoing.