Microsoft has a Terminal Services Advanced Client that is a html file and an activex control. Well, just checked, guess that is no longer available. But here is what looks to be the same thing. Remote Desktop Connection Web Connection. Now I do not know exactly what an activex control is, but maybe this will help.

Note: It says it needs to be served for IIS, but if you are using it on your own computer, just putting it in a directory and loading the html file in a browser will work w/o a problem.