Yes. You need to fill in a disembarkation card like this that you get while on the plane (+ you get a customs declarations form as well):
They stick the embarkation part into your passport and you need to give that to them when you're going back to the UK.
Sorry, looking at this again and I'm wondering some things:
For the left side: Flight number is just whatever the flight we're on number is right?
Right side: Flight Number is the flight we're getting home (aka proof of our transport out of the country). And the intended stay. Do you put the day you're leaving (so 2016, 04, 11 for me). Also being unemployed won't affect anything will it? (since they ask for your occupation >.> )
Finally, can you get another one if you mess up/do they give you another one if it's hard to read (in Japan)? Because both mines and my SOs handwriting is rather hard to read. (to the point where I'll probably just use caps for the whole thing and pray I don't mess up/don't make my letters to big since boxes like this I usually can't fit everything in >.> )
I hate being worried about nothing (probably) but my brain can't help but think of everything that could go wrong >_>