"In response to this illegal action, Prime Minister (Shinzo) Abe and I had agreed to work together and with others in the worldwide community to strengthen pressure against North Korea including by increasing the pace of sanctions".
As she arrived in Japan, Mrs May said: 'We are very clear that the actions of North Korea are illegal.
Japanese Prime Minister Shinzo Abe and British counterpart Theresa May will "work to quickly establish" a bilateral trade partnership with an eye to the U.K.'s coming divorce from the European Union, they said in a joint statement here Thursday.
'We will be re-doubling our efforts with our global partners to put pressure on North Korea, to stop these illegal activities.
"I think we will give businesses certainty, which is what business wants at the point at which we leave".
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The British leader said she and Abe had agreed to work with others to step up pressure on North Korea, including a speeding-up of the implementation of sanctions. They are our closest partner in Asia.
Her first official trip there as comes at a tricky time, a day after North Korea's missile launch over Japan, and just as Brussels ratchets up its criticism of Britain's Brexit negotiators. "We must work together to enhance our collective response to the threats to the worldwide order and global peace and security", she said. "And that must include confronting the threat that North Korea poses and ensuring that this regime in North Korea stops its aggressive acts".
She and Japanese Defense Minister Itsunori Onodera met on the Izumo at a naval base in Yokosuka, south of Tokyo.
North Korea outraged the worldwide community with its latest missile test yesterday.
A 15-strong delegation of UK business leaders, along with International Trade Secretary Liam Fox are flying out for the visit and will attend the UK Japan business forum in central Tokyo, where the PM will make a speech. She is to meet Emperor Akihito on Friday before leaving.