Earlier this month the United Nations Security Council unanimously agreed to impose sanctions on North Korean exports that were likely to cut the country's $3 billion annual export revenue by a third.
North Korea launched a missile late on Monday. "We see that the best way of doing that is for China to be bringing pressure to bear on North Korea", May told reporters on her way to Japan for meetings with Japanese Prime Minister Shinzo Abe.
Tokyo and London also pledged to work with the worldwide community to strictly implement the United Nations Security Council's sanctions on North Korea with a view to bring about its denuclearization, according to the statement.
Speaking before starting her journey to Japan, she said: "These are illegal tests, we strongly condemn them and we will be working with Japan and other global partners to ensure that pressure is put on North Korea to stop this illegal action".
She, however, dodged questions when asked whether the United Kingdom would commit troops to deter them, and declined to specify any red lines for North Korea. In July, Chinese Foreign Minister Wang Yi warned that sanctions against North Korea were "needed" but "not the final goal".
China shrugged off May's intervention, which came after Kim's regime fired a ballistic missile over the Japanese island of Hokkaido.
Earlier this month, North Korea said it was planning to launch four Hwasong-12 rockets that would fly over Japan and hit the water around 30 to 40 kilometres away from the USA territory of Guam in the western Pacific. "They have leverage on North Korea, and I believe we should be encouraging China to exercise that leverage".
The missile was sacked on Tuesday, amid an 11-day US-South Korean military exercise on the Korean Peninsula that North Korea had protested against.
Britain and Japan are aiming to put in place a bilateral trade agreement "pretty much immediately" after Brexit, a government source said on Thursday as Prime Minister Theresa May tries to reassure businesses and politicians during a visit to Tokyo.
The PM wants to use the trade agreement being finalised between the European Union and Japan as the basis for a future pact with the Britain.