The British prime minister visited Saudia Arabia, defying its strict female dress code by dressing in a dark blue button suit with her wrists and ankles covered but without a head scarf.
On trade, the Prime Minister is expected to explore ways of boosting the already very strong UK-Saudi ties.
May and Saudi King Salman held talks focused on “bilateral relations and cooperation” as well as “regional and global developments”, the official news agency SPA said.
Likewise in Saudi Arabia, she said: “We must never forget that intelligence we have received in the past from that country has saved potentially hundreds of lives in the UK”.
Saudi Arabia is now the UK’s largest trading partner in the Middle East, with exports of British goods standing at £4.67 billion and services at £1.9 billion in 2015.
“Britain must halt arms sales to Saudi Arabia immediately, throw its weight behind a ceasefire resolution at the United Nations and back a full and genuinely independent investigation of the evidence of war crimes in Yemen”.
The premier also said her presence in Saudi Arabia would show “what women can achieve”.
“What we are doing is continuing the links that we have had for a long time with countries that are important to us around the world” she told the BBC. Former US Secretary of State Hillary Clinton and former first lady Michelle Obama also chose not to wear headscarves during their visit to Saudi Arabia.
“The new administration being a pro-business administration I think will realize that business in Saudi Arabia will create benefits in the U.S.in terms of job creation”, said Prince Saud.
Jordan and Britain are part of the US-led coalition that has been carrying out air strikes and supporting local forces against IS in Syria and Iraq since mid-2014.
May has come under fire over her foreign trips since becoming prime minister a year ago.
She has faced calls at home to raise rights issues with the kingdom’s leaders, primarily over Britain’s arms sales to a Saudi-led military coalition battling Iran-backed rebels in Yemen since March 2015.
But left out of the picture are the human rights organisations and campaign groups that want Mrs May to use this visit to pressure the Saudis to both end their military campaign in neighbouring Yemen and to release three young prisoners held on death row.
A British government spokesman said May had made a “personal choice” and a source travelling with the prime minister said it was intended as a “statement”.
Asked if May would be raising the issue of Yemen during the visit, her spokesman said it was “not on the agenda”.
May also pointed to social reforms announced in the Vision 2030 programme, including plans to increase women’s participation in the workforce from 22 to 28 percent by 2020.