Warwick’s Law and Sociology is a BA, but it usually includes the main core law modules. If you take all of them, it might still meet the requirements for the solicitor route, though this can change a bit each year.
I’d suggest emailing the Law School undergraduate office. They can confirm whether your entry year’s version is still a Qualifying Law Degree and tell you which modules are needed.
It’s also good to check the module list on the website first, so you know exactly what to ask.
If your main goal is to become a solicitor, a single LLB might be the safer route. But if you’re interested in both law and sociology, the joint degree could still work well once you confirm the details.