I realized after applying that I'd chosen the wrong course

I chose to do law in university. I was never passionate about law, I was thinking practically and decided the only courses I'd be interested in doing were maths, economics, engineering, or law and law is what I eventually settled on. A significant reason for choosing law is that my school was nagging me to apply to Oxbridge, and I don't do FM or physics which ruled out doing maths, economics, or engineering at those unis. If there was a way I could apply for law at Cambridge and maths, economics, or foundation years in engineering somewhere else I would have done that. But since I could only write one PS of course, applying to study law at Cambridge meant I had to apply to study law everywhere. I ended up getting rejected from Cambridge, so now I'm stuck with an application (and offers) to study a course I have no real interest in.

I don't know what to do. I really don't want to take a gap year and reapply. If I could switch to doing maths (or really any of the other courses I mentioned) in uni that would be the best case scenario but idk if that would be possible and I don't want to be stuck doing law or having to drop out. I could reject my offers and go into clearing, but idek if those courses will be in clearing. This is annoying.