BAE, Britain's leading defense company, is particularly keen to make a big score in the Persian Gulf, one of the United Kingdom's most strategic arms buyers, after the October collapse of a proposed to merge with European aerospace giant EADS.
Cameron flew first to Dubai and Abu Dhabi, the financial and economic powerhouses of the emirates. He reportedly hopes to persuade Abu Dhabi, which controls military procurement for the seven-state federation, to buy 60 Typhoons in a deal likely to be worth $4.8 billion.
The Emirates has long been considering the purchase of up to 60 French Rafale multipurpose jets built by Dassault Aviation to replace its Dassault Mirage-2000s.
In Dubai, Cameron's first stop, he toured the al-Minhad air base with senior emirate officials inspecting air force Typhoons, produced by the Eurofighter consortium, that are there on a training exercise.
But Cameron and his high-powered team were preceded in the gulf by French President Francois Hollande, who was hosted by the Saudis Sunday and pressed the Emirates to buy the Rafale.
Cameron also wants the Saudis to add to the fleet of 72 Typhoons they bought for $8.6 billion in 2009 and are still being delivered. There are reports Riyadh is interested in buying another 48-72 Tranche 3 Typhoons, a deal worth $7.3 billion-$11.2 billion.
However, the Saudis are committed to buying 84 Boeing F-15S fighters and dozens of helicopters from Boeing and Sikorsky Aircraft, a division of United Technologies Corp., for $33.4 billion as part of a massive U.S. arms package to counter Iran.
So it's not clear whether Riyadh's prepared to sign up for another multibillion-dollar combat jet purchase from Britain -- not without some sort of quid pro quo, at least.
Meantime, the sultanate of Oman, on the southeastern tip of the Arabian Peninsula and a longtime British ally and arms buyer, is reportedly negotiating to acquire 12 Typhoons.
Britain controlled the Gulf Arab states until 1971, then, its imperial power ebbing, it withdrew all its military forces from east of the Suez Canal. The United States filled the security vacuum left by the British.
But sales to Saudi Arabia, the Emirates, Bahrain and Oman in particular remain vital to Britain's defense industry.
Cameron, who's been annoyed by claims he uses his overseas trips to sell arms and defense systems to countries with questionable human rights records, reportedly insisted on minimizing media coverage of his swing through the gulf.
Even so, he declared in Dubai Monday: "On human rights, there are no no-go areas in this relationship. We discuss all of these things but we also show respect and friendship to a very old ally and partner.
"We have one of the strictest regimes anywhere in the world for sales of defense equipment but we do believe that countries have a right to self-defense and we do believe that Britain has important defense industries that employ over 300,000 people, so that sort of business is completely legitimate and right."
That may go down well in the gulf but Cameron and his increasingly shaky Conservative-Liberal coalition still face growing criticism at home for selling arms to autocratic states that are clearly resisting the pro-democracy surge across the Arab world.
"The U.K.-U.A.E. ructions highlight a broader problem facing London's diplomacy in the gulf," the Financial Times observed.
"While the United States is insulated by the security cover it offers the monarchies against Iran and other potential threats, Britain's more vulnerable position was exposed again last week when Saudi Arabian officials condemned a decision by a U.K. parliamentary committee to investigate the relationship between London and Riyadh."
There has been growing criticism in Britain of alleged human rights abuses and the lack of accountability in Saudi Arabia and the Emirates, particularly as these monarchies struggle to keep the pro-democracy uprisings of the so-called Arab Spring at bay.
The recent crackdown on Islamist groups in these states has intensified the criticism at a time when seemingly moderate Islamist governments are emerging in North Africa.
2014: NFL Cheerleaders [PHOTOS]
Navy tests MQ-8C unmanned helos