Who is responsible for releasing each new version of HTML?

There is an official HTML standards organization, called the World Wide Web Consortium (or W3C), see related link.

HTML versions are released as specifications, papers that describe which tags are valid and how they should work, and those specifications are released by the W3C.
But the specifications are just paper, and it is up to the browser vendors to implement the standards - they may implement bits they like, ignore bits they don't like and add bits they think are missing.
In the real world, the HTML versions we use are not controlled by any single organization. Historically, the standards have sometimes played catch up by just writing down what the browsers are already doing, and sometimes proposed stuff that has been universally ignored.

So the responsible would be the W3C, the 3-4 major browser vendors and the interaction between them. It is hard to be much more specific than that.