* Abe says does not want overnight Brexit cliff edge
* Abe says overnight rule change would sow confusion
* May has said she wants UK to be best place for business
* Japanese companies are major investors in the UK (Adds quotes and detail)
By Guy Faulconbridge and William James
LONDON, April 29 (Reuters) - Japan's Shinzo Abe called on Prime Minister Theresa May to ensure a smooth transition for business as the United Kingdom leaves the European Union, to avoid a cliff edge where rules and regulations for firms change overnight.
A day after talks with May at her country residence at Chequers outside London, the leader of the world's third largest economy made clear his concerns over Brexit while also underlining his long-term commitment to the United Kingdom.
Japanese companies including carmaker Nissan and conglomerate Hitachi have invested more than 40 billion pounds ($52 billion) in the United Kingdom. Japanese companies employ a total of 140,000 people in the country.
"When the UK leaves the EU, if the rules change overnight, there will be a concern about a possible confusion arising," Abe told reporters in London.
Abe added that he wanted the UK to prioritise "a smooth and transparent process including setting a transition period."
The outcome of the Brexit negotiations will shape the future of Britain's $2.6 trillion economy, the world's fifth biggest, and determine whether London can keep its place as one of the top two global financial centers.
Since the shock June 23 Brexit vote, Japan has expressed unusually strong public concerns about the impact of Brexit on the United Kingdom, the second most important destination for Japanese investment after the United States.
May has said she wants what she calls a "phased implementation" for Brexit, though she has two years of complicated negotiations ahead with 27 other members of the European Union over how that would work.
While many diplomats and chief executives say they expect a Brexit divorce deal to be struck, there are thousands of complicated trade, financial and other regulations which need to be clarified to ensure trade is not interrupted when the United Kingdom leaves at the end of March 2019.
And though leaders have repeatedly said it would be in the economic and security interests of both the United Kingdom and the European Union to strike a deal, there is concern in financial markets that the talks could be derailed by politics.
"Japan supports a strong UK and a strong Europe," Abe said. "It is necessary that the firm solidarity of Europe as a whole is maintained while ensuring a smooth and successful Brexit," Abe said.
After talks with Abe on Friday, May said she wanted to ensure "the UK remains the best place in Europe to run and grow a business, whether it's one operating at home or abroad."
May mentioned SoftBank's purchase of Britain's most valuable technology company ARM, Nissan's commitment to build the new Qashqai model at their plant in Sunderland and Toyota's 240 million pound investment in Derby as evidence that Japanese business was confident about Brexit.
May has said she wants a Brexit deal which will enable Nissan and other automakers to flourish in Britain, and last year the Japanese company said it had received assurances allowing it to increase production at its plant in Sunderland, northeast England. (Editing by Alistair Smout and Toby Chopra)