I don't know if there is a new solution, but we did that using https://msdn.microsoft.com/library/microsoft.windowsazure.storage.blob.cloudblobcontainer.listblobs.aspx - if we see what is going on with Fiddler, there are only prefix-ed blobs returned. Please see if that will work for you:
static void GetBlobsByPrefix(string Container, string Prefix)
{
if (!string.IsNullOrEmpty(Prefix))
{
var _Container = GetBlobContainer(Container);
var _Blobs = _Container.ListBlobs(Prefix, true);
foreach (IListBlobItem blob in _Blobs)
{
....
}
}
}
static CloudBlobContainer GetBlobContainer(string container)
{
CloudStorageAccount _StorageAccount = CloudStorageAccount.Parse(
CloudConfigurationManager.GetSetting("rus_AzureStorageConnectionString"));
CloudBlobClient _BlobClient = _StorageAccount.CreateCloudBlobClient();
CloudBlobContainer _Container = _BlobClient.GetContainerReference(container);
return _Container;
}