You cannot say that people in Derbyshire are a different race from people in Yorkshire, so your example would not constitute racism, just ignorance and bad manners.
I was born in Yorkshire, and all my family were Yorkshire born and bred, ("Yorkshire born and Yorkshire bred, strong in the arm and thick in the head" as the quote goes. Ooops is that racism? Can you be racist against your own people I wonder? ) and most Yorkshire people proudly consider people from anywhere else to be not simply another race but oftentimes a whole different species!
I think that any race of people can be racist, it is not simply a matter of colour difference. From my time spent in Wales I have been shown that prejudice between same colour but different race is very much alive and flourishing.
"The only people the Welsh hate more than the English are the Irish." This is a quote from one of the very first people I met when I moved down here, I thought he was joking, but during the last 8 years I have realised that unfortunately he was not.
I had not thought about Wales as a seperate country in all the time I lived in Yorkshire, it was simply a part of the British Isles, like Scotland and Northern Ireland. I did not know that they were unhappy about it, or that they wanted to be a seperate country, not until I moved here and realised all the different ways there are of seeing your race, country of origin and indeed your nationality.
It is much more complicated than colour and creed, and it is a serious issue that gets more tangled and confusing the more you try to get to the bottom of it.