Thanks for the replies. I realise what I was looking for now is called a coaxial indicator.

For ref, I have a Sieg X3 with chuck, and recently a rotary table.

I bought one of these from Allendale Electronics. I've pretty much discarded the Chinglish instructions and just having a play with it.
Click image for larger version.  Name: me-dial-cent_main.jpg  Views: 1166  Size: 66.7 KB  ID: 3214
My only gripe so far is that it shows ~0.01mm movement without a probe attached. Is that a defect or to be expected?