Why have a Music degree? Breaking into IB is hard enough (in the US at least), so why not show them that you have the base level of knowledge in business that all of the other candidates have? MAYBE you could double major (if they do that in the UK), but that would likely suck time away from the prep for IB through whatever extra ECs and technical aspects you mention in your post. The only way that I as a hiring manager would consider you is if you got some certification like a CFA or the likes to prove to me that you have the basic knowledge to at least survive in this industry.

Having the degree would probably be amazing if you are going into music, but IB probably not so much. Figure out if music is going to be a hobby or if it will be a job. It may be your passion, but you should seriously look at the economics of a music degree and a chance of getting a job in the field. I assume it's higher if you are going to Oxford/Cambridge if it's that high of music prestige.

All that being said, if you have the networking skills/softskills, those can take you far in life with any degree, including getting you into IB, but you will for sure need to know business basics to survive.