Japan already stated that they are very interested in the METEOR and BRIMSTONE missiles.
There are other fields related with but outside of the defence sector where the UK and JAPAN have similar interests like Space, commercial aviation and other tech sector related industries.
If the UK & Japan think outside of the box a little there are numerous examples where they could cooperate better and both make some good money.
High speed trains and railways, radar tech and even shipbuilding to name a few.