This depends greatly on what your degree is in. For example, if you study law in Scotland but wish to practice in England, you may be required to do an extra year of study in order to be qualified to practice in England.
If you study something in STEM or other fields, it's very likely that no one would even give it any thought! Many companies these care more about what you can do than where you got your degree.
So the answer is it depends - what would you like to study at university?