Physics Undergrad Engineering Grad?

Hi, I'm rather at a loose end at the moment.

I'm currently studying A Levels in Mathematics, Further Mathematics and Physics as a home student whilst working full time. I am stuck between the options of doing a degree in either Physics or Engineering (most probably electrical). I've been going over the possible outcomes over and over again but I honestly can't decide on which I would rather do. Is there a possibility of studying Physics at undergraduate and then moving onto a Engineering degree at graduate level, or vice versa?

P.S. I'm learning a diverse range of subjects at home as I want to eventually work with technology innovation for the future, including computer science, chemistry, business and economics. Just so you have an idea to where I want to go.

Thanks