I sought an employment lawyer's advice on this once (as part of a larger question). The scenario is heavily affected by common law. I am guessing (as this is HN) that you are working in technology. The way it was described to me is that if you work in, say, banking, and you make your own banking app on the side, this could be argued to be "in the course of your employment". If you made a video game however (or something else unrelated to the business), the law is likely to side with you.
My best advice is to be transparent with your (potential?) employer (assuming you have nothing to hide) and let them know what you do outside of work hours and see if they will amend your contract suitably. If not, spending £250-300 for an hour of an employment lawyer's time is worth it and is likely to resolve your question.