As of 1 February 2019 the UK is part of the new EU-Japan Economic Partnership Agreement.
This is the largest agreement that the EU has ever negotiated. Japan is the world’s fourth largest economy with a population of 127 million. It is the third largest consumer market in the world. When the UK leaves the EU, we will also leave this and all of the 40 other trade agreements that the EU has negotiated.
The UK has so far reached agreement to continue trading with Chile, Eastern and Southern Africa (Madagascar, Mauritius, Seychelles and Zimbabwe), the Faroe Islands, and Switzerland (plus Liechtenstein). And there is now a Mutual Recognition Agreement with Australia and another with the USA.
The Department for International Trade is also trying to establish a set of post-Brexit tariffs for the UK that the other 164 members of the World Trade Organisation will accept.