I am looking for someone who can clear this quiry.
Besides LLM, these combined programs, such as Law & Accounting, Law & Finance, Law & History
are they more preferred by law firms? If solicitor firms do not care about LLM, why so many ppl who are not going into academia want to do it? esp. Oxbride, LSE?

The top prgrammes are taken by prospective BVC/LPC students because they add something to their CV. An Oxbridge/LSE/UOL LLM can show some specialism and also the ability to use the law at a very high level. To be honest, I wouldn't think that solicitors firms would really look for any of the combined programmes that you listed but I'm not sure.