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.
North Korea on Tuesday fired a Hwasong-12 missile - reportedly capable of carrying a nuclear payload - that traveled almost 2,700 kilometers into the Pacific and triggered alert warnings as it flew over northern Japan.
Landing in Japan just 36 hours after Pyongyang sent a missile over the north of the country, the Prime Minister insisted the United Kingdom would be re-doubling its efforts to curb the regime's weapons testing programme.
"What I want to do is work with our global 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".
"Building on our existing ties with friends and allies around the world is vital as Britain prepares for a new era outside the European Union", May said Wednesday ahead of her trip.
South Asia monsoon flooding kills 1200, displaces millions
There are still people who remain missing in the area and diseases have begun to spread in the slum areas submerged in water. The monsoon season in South Asia lasts from July till September every year.
Japan's Prime Minister Shinzo Abe called it an "unprecedented" threat to his country, while US President Donald Trump said it was an act of "contempt".
The UK can not negotiate bilateral trade deals until it leaves the European Union in 2019.
Pyongyang has tested a barrage of missiles over the past years, but it is the first time it launches what is believed to be a ballistic missile over Japan.
Mr Abe will be seeking assurances from Theresa May that Brexit will not be detrimental to Japanese businesses with bases in the UK. "But crucially, we see China as being the key in this", Theresa May added. In terms of what's we're doing, we're looking to work with our partners. She is to meet Emperor Akihito on Friday before leaving.
He told Abe that the Seoul government immediately convened a National Security Council meeting to denounce the launch and had four Air Force fighters conduct a bombing exercise in a show of force, which he called the highest level response South Korea has taken.