Newspaper report accuses BAE Systems of paying billions of dollars to Saudi prince.
Analysts said that if the deal included weapons and long-term maintenance of the aircraft as well, the value could rise to about $40bn.
Tony Blair, the British prime minister at the time, said that the probe would harm national security.
Britain’s Guardian newspaper accused the arms contractor of paying Prince Bandar bin Sultan, son of the defence minister and Crown Prince Sultan, nearly $2bn over two decades in connection with a 1985 arms deal.
The al-Yamamah deal, which provided Hawk and Tornado jets plus other military equipment to Saudi Arabia, was one the the biggest export deals in British history, worth an estimated $86bn.
Bandar, a former Saudi Arabian ambassador to the US and secretary-general of the Saudi National Security Council, has denied the sums involved represented secret commissions to him.
BAE has also denied making any wrongful payments.
In June, the US department of justice launched an investigation into BAE’s compliance with anti-bribery laws, including its past dealings with Saudi Arabia.
Saudi Arabia will pay the same price for the Eurofighter jets as the British air force, the statement from the Saudi defence ministry said on Monday.