I'm certainly not denying that all law firms are selective, although brokenhearted's own post would suggest that it's not only the ones who pay for vocational training who are picky. However as other posters above have confirmed it is categorically not true that you have to have gone to a public school and or Oxbridge, or to have got a first, in order to have the 1 or two years of vocational training paid for by the firm.
To be clear, we take a mix of law and non law students. It is not "better" to have done a subject other than law, but neither does it put you at a disadvantage where training contract applications are concerned. If the non law subject has relevance to a type of law or a client sector then you might be better off doing that. For example if you want to be, say, an IP lawyer, then a first degree in a science might give you an advantage if applying to specialist IP firms. (In fact they often take people with PhDs).
The non law students apply before they have their final results just like the law students do. It's just that the non law students start work a year later than the law students who applied at the same time. Offers are usually conditional upon getting a 2:1.
Actually we are also seeing more and more students who are doing joint honours with English law and another subject and spreading their degree over 4 years.
However I have hijacked the OP's thread, simply because I couldn't let brokenhearteds comment slide.
OP, of course it's fine to study law and not want to be a lawyer. It is an academic subject in its own right - who do you think taught us at University? Not practising barristers and solicitors but men and women who had devoted themselves to the academic study of law as a career.
One of my university contemporaries never practised a day in her life and instead became a successful journalist. Others are civil servants and HR professionals, supermarket area managers, run their own businesses - law impinges on every part of life.
However I suppose my question to you would be, why are you studying anything at all - is it for a career or just purely for interest? If you are doing your OU degree to help you get a better job, you might find that something else is better than pure law. Some courses do still have a law element in terms of the law applying to that particular area eg law for social workers, or journalists.
Anyway best of luck and enjoy your studies.