He also stressed the Philippines' sovereign rights over Benham Rise, a vast offshore frontier off his country's northeast. "I'll just keep quiet", Duterte said.
Duterte was referring to the country's 200-nautical-mile exclusive economic zone, a stretch of sea where coastal states have been granted exclusive rights to exploit natural resources under a 1982 United Nations treaty.
Foreign ships can pass but cannot fish or extract oil and gas from the under the seabed.
Under the BCM, officials from Philippine and Chinese foreign ministries and maritime affairs agencies will meet once every six months. It is roughly the size of Greece and believed to be rich in biodiversity and tuna.
Roque said that the Philippine delegation will be led by DFA Undersecretary for Policy Enrique Manalo while the Chinese delegation will be led by Vice Foreign Minister Kong Xuanyou.
During the meeting, the Philippines "brought up our territorial claims and sovereignty rights issues, and discussed how to manage and prevent incidents on the ground".
Mr Williamson said it was right for countries such as the United Kingdom and Australia to "assert our values" in the South China Sea, a lucrative trade route, which is also claimed by Brunei, Malaysia, the Philippines, Taiwan and Vietnam.
"Both sides agreed to continue discussions on confidence-building measures to increase mutual trust and confidence and to exercise self-restraint in the conduct of activities in the South China Sea that would complicate or escalate disputes and affect peace and stability", the statement said.
Speaking of Britain's controversial plan, China's Foreign Ministry spokesman Geng Shuang reasserted China's insistence that its territorial claims do not conflict with worldwide law when it comes to freedom of navigation and overflight.
Dozens of left-wing activists protested Saturday in front of the Chinese consulate in metropolitan Manila, some wearing red boat-shaped paper hats with the Chinese flag's markings and the message: "China out".
China claims almost all of the South China Sea and has been in a building binge in the area, turning reefs and islets into islands with runways and various other facilities and buildings.
Mrs May said her visit had marked Britain and China "opening a new chapter in our golden era", with commercial deals totalling £9 billion signed.
"China is seeking to overturn the rules of worldwide order".
Roque said that the BCM was established based on the joint statement issued after President Rodrigo R. Duterte's landmark visit to China in October 2017.
Mr Williamson added in an interview with broadcaster ABC on Tuesday: "It's very important that we demonstrate that these are seas anyone can pass through and we'll be making sure that the Royal Navy will protect those rights for worldwide shipping".