Legal aid is pretty well a thing of the past. It used to be that the poor could get it for everything. Now, it's almost impossible to get. Civil matters are dealt with on a contingency fee basis. Family law (divorce, etc.) -- if you're a woman and your husband is beating you, you might get it. Otherwise it's tough titty.
Criminal law, you'll get it if the case has a serious risk of a custodial sentence. Otherwise, again, tough titty.
You're right about the police not giving a fuck about most possession cases though. Two stories from the early 90's. A friend and I had been shopping in a fashionable boutique. We hadn't bought anything, but we obviously attracted some attention. When we came out, we were stopped by two cops who wanted to search us. I had a quarter ounce of weed in my pocket. They had me turn out my pockets and my bags. You couldn't miss that bag of fat stinky weed I had. It took up the whole of my hand. They just weren't interested. Hadn't stolen anything, so we were free to go.
Another story. Again from the 90's. A friend had a water leak in his flat. The neighbour called the water people to come and break into his flat to stop the leak. We was by-passing his electricity meter. He also had a couple of ten pound bags of heroin on his kitchen table. They found the meter, charged him with abstracting electricity. Weren't arsed about the heroin. Not worth their time.
Of course, if you act the cunt or if their after you for something else, you're definitely getting charged -- but it hasn't been a foregone conclusion for years and years and years now. They know the courts are just giving you a slap on the wrist -- why would they be bothered?