According to Wikipedia (and yes I know you can't always trust it!) the Imperial Japanese Army obtained a number of WW1 tanks immediately post-war for evaluation. One of these was a Mark V, and there were a number of Whippets and some Renault FT-17s. Don't suppose anybody has any more information on the Mark V do they?
I emailed the Yasukuni shrine and a very helpful Mr Noda replied to say that it arrived in October 1918 along with 4 NCOs and a Major Bruce as instructors - these worthies were decorated by the Emperor on their return to the UK. The seem to have stayed with it at the army driving school at Setagaya for a while
According to a diary at Yasukuni in 1937 it "won the favorable reception of the viewer" - which probably makes it more popular than most of the UK commemoration tanks in the inter-war years which had of course been sliced up for scrap by then!
The other thing is that it is unclear what actually happened to the tank at the end - he assumes that it was disposed of during WW2 or just after.
(Many thanks are, I think, due to Noda San for his reply)