May is scheduled to sit down with Toyota's chairman during her three-day tour which starts in Osaka before moving to Tokyo where she meets with Emperor Akihito and Prime Minister Shinzo Abe, who visited Britain this year.
Britain formally told the EU in March it will withdraw from the 28-member bloc, stirring fears in Japan about what the move would mean for companies with significant business interests in the country.
More than 1,000 Japanese companies do business in Britain, employing some 140,000 local people with many using Britain as as a staging post to do business in Europe.
Among them, automakers Toyota and Nissan have factories in Britain while tech giant SoftBank last year announced the $32-billion purchase of British iPhone chip designer ARM Holdings.
But Britain is now at risk of losing the "passporting rights" financial firms use to deal with clients in the rest of the European bloc.
Japanese megabank Mitsubishi UFJ has said Amsterdam and Paris were favourites to be the new European base for its securities operations.
Brokerage Nomura, Daiwa Securities and Sumitomo Mitsui Financial Group are planning to move their main EU bases from London to Frankfurt.
Britain's foreign minister Boris Johnson boasted about Japan-UK investment when he visited this summer, but local firms will be looking for solid assurances from Britain's leader, who is traveling with a business delegation.
"But if that isn't an option, we are saying we need a transitional period... To mitigate the negative impact," he told AFP.
May -- who is to attend a traditional tea ceremony in Kyoto and a dinner on Wednesday -- will also be discussing issues tied to global terrorism and regional security, after North Korea sharply escalated regional tensions by launching a ballistic missile over Japan on Tuesday.
"The prime minister is outraged by North Korea's reckless provocation and she strongly condemns these illegal tests," a spokeswoman for May said Tuesday.
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