I think you'll find what you're looking for here Link to B4A Forum post, you need to get the HTML to a string first, then load it to the web view with webview1.LoadHtml(s) (if you still want to). The first code example is enough for what you want.
You'll need to download the HttpUtilsExample.zip attached to the post and add the HttpUtils and HttpUtilsService modules to your project and enable the HTTP library.
Once you've got the modules in place the 'main' module should look like this:
'Activity module
Sub Process_Globals
'These global variables will be declared once when the application starts.
'These variables can be accessed from all modules.
End Sub
Sub Globals
'MY ADDED LINE
Dim Webview1 As WebView
Dim b4a As String
b4a = "http://www.basic4ppc.com"
End Sub
Sub Activity_Create (FirstTime As Boolean)
'MY ADDED 2 LINES
webView1.Initialize("Webview1")
Activity.AddView(Webview1,0,0,100%x,100%y)
HttpUtils.CallbackActivity = "Main" 'Current activity name.
HttpUtils.CallbackJobDoneSub = "JobDone"
HttpUtils.Download("Job1", b4a)
End Sub
Sub JobDone (Job As String)
Dim s As String
If HttpUtils.IsSuccess(b4a) Then
s = HttpUtils.GetString(b4a)
'MY ADDED 2 LINES
Log(s)
Webview1.LoadHtml(s)
End If
End Sub