C# - How To Capture File Upload Data From Webpage

I'm well aware of how to get files from the client to the server using standard ASP.NET techniques, however, I have a need to be able to retrieve data from a third party web page written in basic html and process the file data in an asp.net web application.

So if the basic html looks like this...

<form id="form1" action="WebForm.aspx" method="post">
<input name="fileUpload1" type="file" enctype="multipart/form-data" />
<input type="submit" value="click" />
</form>

How do I retrieve the file data in the page referenced in the action attribute of the form. So far I have tried the code below, which allows me to access the file name - but not the byte stream of the file.

protected void Page_Load( object sender, EventArgs e )
{
string fileName = Request.Form["fileUpload1"];
// No files appear in the request.files collection in code below.
foreach (string file in Request.Files)
{
HttpPostedFile hpf = Request.Files[file] as HttpPostedFile;
if (hpf.ContentLength == 0)
continue;
string savedFileName = Path.Combine(
AppDomain.CurrentDomain.BaseDirectory,
Path.GetFileName( hpf.FileName ) );
hpf.SaveAs( savedFileName );
}
}