Job Prospects

Hi, I am a 22 year old LLB graduate from a non-RG uni. I have been working in resi conveyancing for the last year (started straight out of uni last may). I would like to get a training contract. Hopefully in commercial property but open to other suggestions
. My current firm have made it clear that I would not obtain a TC from them but CILEX was an option (no cost to me). My question is how realistic are my prospects at getting a TC given that I went to a non-RG uni and how would you go about getting one.