Something to note is you don't even have to do the conversion course if you want to become a solicitor necessarily, you would take the SQE instead. You only need to do the conversion course to become a barrister.
If you are at all uncertain about your possible future in law I'd robably say do a different degree in something you're really passionate about - even if that thing isn't necessarily a professional course itself (e.g. classics, anthropology, palaeontology, planetary science, etc). Then pursue legal work experience on the course and see how it suits you. Law degrees are pretty dry I gather and also tend to have a relatively low first rate, so if you have other interests you want to pursue as well by all means go for those initially!
A law degree =/= a law career at the end of the day. Do the degree if you're interested in law as an academic discipline - if you just want to do it because you want to become a lawyer then it's not necessary and you can do another subject first and still pursue a career as a solicitor or barrister.