I have recently received an offer for a fully funded PhD in a UK university, but I have also been working in the industry for approximately 10 years, where I currently have a good paying job. I am also planning to go back to the same industry after my studies, so I am particularly interested in not losing touch with it. As a result, I have been considering working part-time (or contracting) during the years the PhD studies will last. My question is whether there could be any legal obstacles in this situation, especially seeing that the offered stipend is not taxed. I would appreciate any advice or references to relevant laws/regulations.

You can work alongside your stipend. If you receive more than the personal allowance in salary, you will be taxed on that, but that won't affect your stipend.

You should probably check the conditions of your grant, I was only allowed to undertake six hours a week paid work.