This is one of those jobs that's easier to do the second time when you've got the knack
Sliding the mirror plate outwards requires strong fingertips against the inner edge and a firm fingertip grip of the outer edge to get it to move against the plastic clip holding it. It's a tight spring fit and will seem reluctant to submit. With the mirror removed, there is then access to unclip the cover
Attached are Jaguar's own instructions for how to do it for the later door mirrors with side repeat indicator incorporated, but the earlier versions use the same procedure.
In passing, perhaps it would have been better to have this thread under the Bodywork heading to help future enquirers find the story. Maybe the Mods can move it
