Japanese Grey Bark Elm is a common name for Zelkova. You are in the UK, correct? We have often seen retailers deliberately misidentify Chinese Elms as Zelkovas presumably in order to skirt restrictions on their importation. Since yours was identified as a Chinese Elm I would tend to believe that ID. At any rate, this side by side comparison should help.
Here is a side by side of Zelkova and Chinese Elm.
The Zelkova is on the left. A US quarter Dollar is about 24MM
Chinese Elms also have some variation in leaf shape, here are some examples.