I have done this for a few projects already.
I would recommend using Pode HTML5 pack for the iframe object. You can place an iframe inside of your project to display whatever website you want to inside of it.
Unfortunately though you cannot add UI on top of any website because of the way things work; like iFrames, text.boxes, buttons, and lists - etc
If you need to have UI on top of the website for some functionality, you will need to do something like build a special version of your site that has the UI buttons you desire. You can maybe take a static image of your site (if it doesn't need all links to work in the project) and scroll it up and down in your project, adding whatever UI elements you want on top since it would be a sprite object.