Will my lack of A Levels be a problem?

I don’t have any A Levels so do you think law firm graduate recruitment teams will just chuck my applications in the bin?

I’m in my late 30s and have just started the second year of my LLB. I am now seriously thinking about applying for training contracts but I as I don’t have any A Levels do you think recruiters will just chuck my applications in the bin? I know I’ve probably got zero chance of getting into a large commercial firm so I’m thinking of targetting smaller ones. Any thoughts will be welcome.