Arriving for three days of trade and security talks, she said the UK had made plain it wanted to avoid a “cliff edge” of sudden and disruptive change for businesses and citizens when it leaves the European Union.
Britain is working with the EU on providing that continuity, she stressed.
She also stressed that leading Japanese firms including Nissan, Toyota and Softbank had already announced significant investments in the UK since last year’s referendum vote to leave the EU.
Britain was also pressing for completion of the EU-Japan trade deal.
Britain regards the deal as a potential model on which to base it’s own deal with Japan after Brexit.
Mrs May added: “There are a number of trade deals the EU has with other countries and we are looking at the possibility of these being able to be brought over, certainly initially, into trade deals with the UK.”
The EU has some 40 trade deals with other countries, of which those with South Korea and Switzerland are currently the most valuable.
Mrs May has travelled to Japan with 15 leading British businesspeople seeking to grow their links with the country.
International Trade Secretary Liam Fox, who visited Japan earlier this year, is also on the trip to meet his Japanese counterparts and potential investors.
Recent reports have suggested Japanese businesses are deeply anxious about the impact of Britain leaving the EU, with one member of the Tokyo government claiming firms have a “sense of crisis” and need “clarity and predictability” from Britain about the process.