Hi Nick,
Is your website responsive, or do you have a separate mobile site?
If it's a separate mobile site, is there a difference between the content on each? If so, I'd have a look at the content and investigate whether the mobile version is more user friendly, for example.
If it's a responsive site, or if the content is the same, I'd investigate the competition. Perform a search for the keyword from a mobile device, and from a desktop device, and check if the websites which are ranking above you on desktop but not mobile have mobile-friendly websites. I've seen this affect some clients more and more, and where we have a mobile-friendly site, that site often ranks slightly better for mobile queries.
Hope this helps, if you do have more information I'd be happy to help some more!
Zoe