Another Doctor Who actor that I met was Peter Davison.
He was in Australia as part of the excellent series of live concerts that Murry Gold was presenting. Peter was live narrating between pieces.
Thanks to my excellent friend Rob Jan, I was taken along on his audio interview to take a couple of pictures, and to monitor the recording.

meeting Peter Davison
meeting Peter Davison

Mr Davison was lovely, and patient and gave Rob a great interview (available on the Zero-G podcast).
I was less professional. Through the course of the interview I became increasing convinced that there was a sound that would be getting packed up of the microphone rubbing against something, and I called halt to the interview at one point to check.
It was fine, and all in my imagination. I did feel stoopid.

Afterwards I didn’t ask to get anything signed (I have the collection of trading cards already). I did ask to have a picture taken, and mentioned how happy we were when he was first announced as the new doctor. He was very polite, but had probably been told similar things for the last 40 years