You can also just add the authorization header yourself.
Just make the name “Authorization” and the value “Basic BASE64({USERNAME:PASSWORD})”
var username = "abc";
var password = "123";
string encoded = System.Convert.ToBase64String(Encoding.GetEncoding("ISO-8859-1")
.GetBytes(username + ":" + password));
httpWebRequest.Headers.Add("Authorization", "Basic " + encoded);
Edit
Switched the encoding from UTF-8 to ISO 8859-1 per What encoding should I use for HTTP Basic Authentication? and Jeroen’s comment.