you know what, you made me doubt myself here so i had a quick search and found various opinions including that the accent is shit on purpose as some kind of satire. thankfully this is bollocks:

https://hypebeast.com/2022/5/the-boys-karl-urban-hypebeast-season-3-billy-butcher

How did you arrive at Billy’s cockney accent?

It’s kind of the perfect storm because you have a British character, played by a New Zealand actor, written by American writers and in the first season I had a Canadian dialect coach. At the end of the first season I identified that there was certain elements of authenticity that could be improved, so I brought in Andrew Jack, who was one of the foremost, world-class dialogue coaches. I had first worked with him 20 years ago on Lord of the Rings. He came in and we significantly improved the specificity of the dialect and he was able to contribute more colloquialisms to give that character more authenticity and I was super excited about where we were going to go, but really tragically he was one of the first victims of the pandemic, he was working on The Batman and he passed

far be it from me to speak ill of the dead but it did not work