Thank you for pointing me in the right direction Krikor.
Still not sure if we can access the components/com_k2/template folder from the Joomla back end interface, but for anyone else with this problem who may stumble across this post, I used Windows Explorer as an FTP client to copy the folder contents and that worked.
I've now made the changes I wanted, so I'm happy. But may I suggest to K2 for the future that having the 'Read More' button at the end of the introtext as a K2 default makes sense from a front-end user point of view.
Thanks again.