As far as I know something like this doesn't exist for UT2004. HTTP isn't the problem, it's actually quite simple, protocol-wise. You can use
El Muerte's LibHTTP to handle that for you.
The real problems start when dealing with the data transported over HTTP: the HTML code, stylesheets, JavaScript and external images. The game does not have built-in decoders for HTML, XML, CSS, JS or any image formats like GIF, JPG or PNG. You'd have to implement all that yourself in slow and limited UnrealScript.
Of course this includes all the work you'd need to put into a layout engine to actually make the parsed HTML look like a web page on the screen.