Are an LLB and a non-law degree from the same uni considered equal?

If i was to do an LLB at a top university like LSE,UCL,Durham,Warwick,Nottingham etc or some form of social science like Sociology,Politics or Anthropology and then a conversion course from the same uni would both degrees hold the same weight?

Obviously providing I obtain a 2:1+ and did relevant legal work experiences and the like while doing a non-law degree?

I’m on the fence as I would like to be a solicitor but I’m not too sure if i’d enjoy an LLB,and also not sure if those “softer” subjects i’ve mentioned (that I would definitely enjoy) would be taken as seriously to employers.

Any advice would be appreciated.