"What I want to do is work with our worldwide partners and I will have obviously have the opportunity in Japan to talk to [Japanese] Prime Minister [Shinzo] Abe about these tests that North Korea have been carrying out, and how we can work together, and with others internationally, to put pressure on North Korea to stop". Britain formally told the European Union in March it will withdraw from the 28-member bloc, stirring fears in Japan about what the move would mean for companies with significant business interests in the country.
But Beijing has today said that war is "not an option" to resolve the issue of North Korea's claims it is getting close to developing nuclear weapons.
"We condemn North Korea in the strongest words possible for a reckless act which was a clear violation of United Nations Security Council resolutions", May told a press briefing during an official visit to Japan.
The British Prime Minister's comments on China's role in de-escalating tensions between North Korea and the rest of the world came during her trip to Japan this week.
Theresa May has reiterated her call for China to put more pressure on North Korea to limit its missile programmes as the United Kingdom tries to get Beijing to participate in imposing tougher sanctions on Pyongyang.
Britain wants new United Nations sanctions against North Korea that would target guest workers sent mostly to Russian Federation and China, and whose wages are a source of revenue for Pyongyang.
China starts radiation monitoring at North Korea border
It was their second phone call of the day and their fourth since North Korea fired a missile over Japan on Tuesday. For context, the bomb dropped on Hiroshima by the US had a 15-kiloton yield.
Her official meetings with Abe and other Japanese officials are scheduled for Thursday in Tokyo. The Council, which was created at the end of 2013, consists of Prime Minister Shinzo Abe and key ministers.
An editorial in the state-run Chinese newspaper Global Times said: 'May's Conservative party lost many seats, turning her into a vulnerable prime minister.
'They have leverage on North Korea, and I believe we should be encouraging China to exercise that leverage'.
North Korea has said that Tuesday's missile test was a direct response to the annual drills, calling it "a part of the muscle-flexing" against the war games. Earlier Thursday, May visited a naval base on the outskirts of Tokyo with Defence Minister Itsunori Onodera before attending a business forum and the security meeting.
British Prime Minister Theresa May will look to ease corporate Japan's worries about Brexit during a three-day visit to the country from Wednesday focused on progress on a bilateral trade deal for when Britain leaves the European Union.