Telling where I am originally from at the first lecture? I am going to start teaching next year in a university in the UK. One common question I get with students in one-to-one conversations is about my origin. I certainly have an accent, and they are naturally curious about it. I was wondering if it is fine that, when I introduce myself during the first lecture, I tell them where I am originally from?  This is not an issue for me.

I understand that some lecturers get offended with the question "where are you originally from?", but I think sometimes students are genuinely interested on knowing this inconsequential information. I was, when I was a student, so I understand.
You can certainly do so. Something like "I was born here. I did my undergraduate degree here, my masters degree here, and my PhD here. After my PhD ..." etc. It doesn't have to be very long and could also be part of your lecture slides.

One of my lecturers from my bachelor's degree did this, and I still remember she and my brother shared an alma mater.