Det lykkedes mig at få et resultat ud af det her.
// Send
HttpWebRequest request = (HttpWebRequest)WebRequest.Create(endPointUrl);
request.Method = "POST";
request.ContentType = "text/xml; charset=utf-8";
request.Headers.Add("SOAPAction", "
http://tempuri.org/getData");
Stream outStream = request.GetRequestStream();
StreamWriter writer = new StreamWriter(outStream, Encoding.UTF8);
writer.Write(envelope);
writer.Close();
// Receive
HttpWebResponse response = (HttpWebResponse)request.GetResponse();
Stream inStream = response.GetResponseStream();
StreamReader reader = new StreamReader(inStream, Encoding.UTF8);
return reader.ReadToEnd();