I've been using UltraEdit recently and just noticed that the new version (13) has a built-in toggle that will let you view HTML files in a browser window within UltraEdit itself. Although the browser window does not automatically refresh when you update code a simple click of the refresh button will accomplish this.
As an HTML/text editor this is a very welcome addition to what is already a very powerful program. The integrated browser is IE, and you can't change to another browser. That's something they may add to future versions. However, you can alternately select to view HTML files in your default browser.