Should I still take degrees that are competitive for a job afterwards?

The one I want to do the most is law and if not that, psychology. I know both of these are hard to get a job after getting the degree so should I still aim to do them?

You're confusing an academic degree subject with the competition for a funded training position after graduation.

Plenty of people study these academic degrees and go into other careers after graduation without a problem. Taking either as a degree doesn't commit you to a specific career.

Although LLB Law courses are vocationally minded, so you're not tied to Law as a career, but the course is mainly there to prepare you for it..

They're really not. In most universities llbs are taught by staff who are law academics and not qualified or practicing lawyers. The postgraduate courses to become a solicitor or barrister are taught by practicing lawyers - but the universities offering LPC/BVC training aren't the same universities that top the law league tables.

One of the main reasons for rejection based on a personal statement is down to applicants focusing on a career in law without any understanding or interest in academic study of law.

Ah, I didn't realise. From what I'd heard from friends LLB courses are designed to fill the 7 areas of Law you have to know about in order to do the bar exam, so I assumed it was largely vocationally-driven. A bit like there's certain stuff we have to do on my course to get CEng status is set in place at the cost of less optional modules, if you see what I mean.