This question covers a lot of ground.
1. The sound isn't an 'r' or an 'l'. The basic Japanese phonetic unit consists of two sounds (excepting the 'a' gyoo, and 'n'). Since there are two sounds in each unit, the initial sound (the 'r') changes based on what follows. 'ri' is not english 'r' + 'i'. The 'r' in 'ri' sounds different than the 'r' in 'ro'. Try making the sounds slowly & feel where your tongue moves from the first sound into the second. You will find the tongue in different locations, giving different sounds.
2. The location of Japanese sound generation is different than American English. What do I mean? I think this is a concept used more in actors trying to replicate an accent, but different cultures have different points in their mouth that the sound 'centers' on. For example, British use the front of the mouth a lot more than Americans. Try replicating a British accent, but move the focus to the tip of your tongue. I bet you will come a lot closer to a 'British' sound. Japanese is much more nasal in its focus. Try moving the focus of your sound generation to the top front of your soft palate & see if it sounds better.
EDIT: Just noticed you are British
So, American English is more centered in the middle of the tongue. Try an American accent centering on the middle of your tongue, flattening it out if you will...
3. I'm curious why you want to sound like a yakuza? Just trilling your 'r' s isn't going to do it.
I'm getting a strange vision of a Japanese trying to replicate a New York ganster accent.. ha! Really, I would advise learning Standard Japanese (Tokyo sound, how newscasters speak, how newspapers are written) before tackling accents. I think you will just sound like a gaijin that can't pronounce the 'ra' row very well.
Accents are notoriously difficult to master. I'm reminded of watching 'On Golden Pond' with someone from New York. They remarked that the actors (Peter Fonda & Katharine Hepburn) sounded just like a New Englander. But to me, the accent sounded 100% fake, since I grew up about 30 miles south of 'Golden Pond'. I was part of the 'in group' for the accent, and could immediately recognize the fake accent.
Sounding 'yakuza' is learning the manners of speech, the phrasing and much more...