I occasionally do recruitment for my firm. And I have to say you'd have to be lucky for me to pick you out of the pile with a 2.1 from the OU particularly with the previous 3rd. Was that a blip? what were your a levels life? Can you explain what happened then and why you've changed now.
Now occasionally I do pick up people who look interesting who don't have the traditional 2.1 from oxbridge/russell group. I am actually slightly more likely to pick up people with 2.2s from a good university, and a good story to tell as I think that the 2.1 is too artificial. It wouldn't make a difference to me whether it was a 2.1 or a 1st though. What would matter would be whether you stood out for other reasons so I read your application and thought about it.
The best I can say about those other reasons to make you stand out are
Get work experience in law, big firms, small firms, high street firms, courts, anything you can. You said you did advocacy representation before. Where? Can you target lawyers who do the same kind of work to get that experience onto your CV. You also have to offer to work for nothing to get that kind of work experience in some places but even a week here and there shows commitment.
Show your commitment. Show that you did the OU degree because you really wanted to be a lawyer, and explain why you really wanted to do it (and don't mention the money at that point!) have you got any particular area that sparked your interest?
Think hard about what type of work you can do well, what does your previous experience help with. If you did representation for say a bank on mortgage reposessions look at people who have general litigation teams (not magic circle). If it was employment representation for HR play to employment lawyers.
Have you got any perosnal networks you can pull favours in from. Who do you know who is a lawyer who may be able to help you out with experience. Even if you don't know them well, if you don't ask you don't get. What about your tutor at the OU, do they have connections. What about mothers at the nursery/ schools?
Also think about local networking events where you might bump into lawyers, lectures, industry groups etc. Visit public hearings, tribuanls courts. Show you really want it and you'll stand out as you may be more commited than the conventional applicant.