"North Korea's recent ballistic missile launch on August 29, which passed over Japan, was an outrageous provocation and posed an unprecedented, serious and grave threat to Japan's national security", the joint statement read.
North Korea's missile programme presents an "unprecedented threat to worldwide security", Theresa May said as she vowed to speed up the implementation of sanctions against Kim Jong Un's regime.
US President Donald Trump also said "all options" are on the table regarding North Korea, ratcheting up his war of words against the Asian nation. It flight-tested two intercontinental ballistic missiles in July and has threatened to send missiles near the USA territory of Guam, where the US has military bases.
May asserted that the global community should try to stop Pyongyang using intense economic and diplomatic pressure. Tuesday's test was of the same Hwasong-12 missile Kim had threatened to use on Guam, but the test flight took it in another direction, over northern Japan's Hokkaido island and into the sea.
Japan's defense budget has been on the rise since Prime Minister Shinzo Abe came to power in late 2012.
Reason: "a ballistic missile launch", said a train station announcement.
"My discussions with Prime Minister Abe will focus on how we can prepare the ground for an ambitious free-trade agreement after Brexit, based on the EU-Japan agreement which I very much hope is nearing conclusion", May said speaking ahead of her visit.
"What they will discuss in private I can't pre-empt, but that is our position and she'll be setting that out if he (Abe) asks", the spokeswoman said.
"If they are applied universally then North Korea will feel the brunt of these sanctions and realise that a penalty has to be paid for its illegal and provocative behaviour", she told Sky News.
The two leaders also agreed to work together to?increase the pressure on Pyongyang, including at the United Nations, and to urge Beijing to play a greater role in the issue, the ministry said.
A No 10 spokesman said: "The Prime Minister told Prime Minister Abe the United Kingdom stood shoulder to shoulder with Japan in the face of North Korean aggression".
The Prime Minister is embarking on a three-day trip to Japan with aspirations to forge a free trade deal similar to the one being negotiated by the European Union with the Japanese.
Previous U.S. administrations and some diplomats within Trump's current government have been cautious about such measures, concerned that they could provoke China into withdrawing what support it has been giving to efforts to pressure its unruly neighbor.