Japan has trade deals with the EU making this possible. The UK will have to renegotiate all those deals themselves (or just copy and paste the old ones? what was the point of independence then?). What happens in the mean time? Is the UK going to remain part of the EU until all those deals with China, Japan, the US - to name a few - are made? It's a huge endeavor and a lot of question marks. I do not envy your position.
There is no free trade agreement yet. There are, however, a number of agreements that cover bureaucracy regarding import and export, as well as other relationships. Maybe most of the UK's non-EU import regulations are negotiated partner for partner by the UK government. In that case, nothing would change. But I doubt that ongoing relationships between global partners and the EU do not have any effect on the UK. See http://ec.europa.eu/trade/policy/countries-and-regions/count... for an overview.
Maybe it's possible for the UK to get custom tailored agreements that are more beneficial. But I'm afraid that until all of that is settled, a lot of time will have passed. Negotiation about the FTA between EU and Japan has been going on for about four years now. Other fora of exchange have been established decades ago. Until the UK can benefit from their own negotiation efforts, the EU might look more attractive to Japanese investments and trade.
International trade is complicated and takes time but the Leave campaign made it look like everything's going to be fine in just a few years.
Hopefully, since that would have the least negative fallout. The untangling of connections across the Channel will take some time.
OTOH, looking at other possible referendums across Europe, I would like it to be clear what an exit from the EU entails as soon as possible. I don't think leave voters will get what they had hoped for, vide https://amp.twimg.com/v/6ca5195b-a8a5-4b20-b209-92440b9a25d6
Honda threatened before to move it's Swindon plant to the continent. They also buy many assambley parts from EU countries. Let's see what happens next.
It is convenint for them to have a plant in UK while UK is part of EU (because they sell UK made cars to EU countries with the current trade agreement) but if agreements change and imported goods from UK to EU get higher price:
- Will Honda keep UK plant to sell higher priced cars to UK (due to higher priced of imported parts from EU)?
- Will Honda move the plant to an EU country to have better prices to a larget market?
How how does this work in the UK advantage, again?