Usa la API UrlDownloadToFile:

in un modulo

codice:
Public Declare Function URLDownloadToFile Lib "urlmon" Alias "URLDownloadToFileA" (ByVal pCaller As Long, ByVal szURL As String, ByVal szFileName As String, ByVal dwReserved As Long, ByVal lpfnCB As Long) As Long

Public Function DownloadFile(URL As String, LocalFilename As String) As Boolean
    Dim lngRetVal As Long
    lngRetVal = URLDownloadToFile(0, URL, LocalFilename, 0, 0)
    If lngRetVal = 0 Then DownloadFile = True
End Function
dovunque ti serve

codice:
DownloadFile "http://www.html.it", "c:\html.html"
Occhio che il download è sincrono, fintanto che non avrai scaricato tutta la pagina la form risulterà bloccata. Ma questo è un altro discorso.

Ciao