Download file inside WebView

    mwebView.setDownloadListener(new DownloadListener()
   {

  @Override  


   public void onDownloadStart(String url, String userAgent,
        String contentDisposition, String mimeType,
        long contentLength) {

    DownloadManager.Request request = new DownloadManager.Request(
            Uri.parse(url));


    request.setMimeType(mimeType);


    String cookies = CookieManager.getInstance().getCookie(url);


    request.addRequestHeader("cookie", cookies);


    request.addRequestHeader("User-Agent", userAgent);


    request.setDescription("Downloading file...");


    request.setTitle(URLUtil.guessFileName(url, contentDisposition,
            mimeType));


    request.allowScanningByMediaScanner();


    request.setNotificationVisibility(DownloadManager.Request.VISIBILITY_VISIBLE_NOTIFY_COMPLETED);
    request.setDestinationInExternalPublicDir(
            Environment.DIRECTORY_DOWNLOADS, URLUtil.guessFileName(
                    url, contentDisposition, mimeType));
    DownloadManager dm = (DownloadManager) getSystemService(DOWNLOAD_SERVICE);
    dm.enqueue(request);
    Toast.makeText(getApplicationContext(), "Downloading File",
            Toast.LENGTH_LONG).show();
}});

Have you tried?

mWebView.setDownloadListener(new DownloadListener() {
    public void onDownloadStart(String url, String userAgent,
                String contentDisposition, String mimetype,
                long contentLength) {
        Intent i = new Intent(Intent.ACTION_VIEW);
        i.setData(Uri.parse(url));
        startActivity(i);
    }
});

Example Link: Webview File Download - Thanks @c49

Try this out. After going through a lot of posts and forums, I found this.

mWebView.setDownloadListener(new DownloadListener() {       

    @Override
    public void onDownloadStart(String url, String userAgent,
                                    String contentDisposition, String mimetype,
                                    long contentLength) {
            DownloadManager.Request request = new DownloadManager.Request(
                    Uri.parse(url));

            request.allowScanningByMediaScanner();
            request.setNotificationVisibility(DownloadManager.Request.VISIBILITY_VISIBLE_NOTIFY_COMPLETED); //Notify client once download is completed!
            request.setDestinationInExternalPublicDir(Environment.DIRECTORY_DOWNLOADS, "Name of your downloadble file goes here, example: Mathematics II ");
            DownloadManager dm = (DownloadManager) getSystemService(DOWNLOAD_SERVICE);
            dm.enqueue(request);
            Toast.makeText(getApplicationContext(), "Downloading File", //To notify the Client that the file is being downloaded
                    Toast.LENGTH_LONG).show();

        }
    });

Do not forget to give this permission! This is very important! Add this in your Manifest file(The AndroidManifest.xml file)

<uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />        <!-- for your file, say a pdf to work -->

Hope this helps. Cheers :)

Try using download manager, which can help you download everything you want and save you time.

Check those to options:

Option 1 ->

 mWebView.setDownloadListener(new DownloadListener() {
        public void onDownloadStart(String url, String userAgent,
                String contentDisposition, String mimetype,
                long contentLength) {
 Request request = new Request(
                            Uri.parse(url));
                    request.allowScanningByMediaScanner();
                    request.setNotificationVisibility(DownloadManager.Request.VISIBILITY_VISIBLE_NOTIFY_COMPLETED);
                    request.setDestinationInExternalPublicDir(Environment.DIRECTORY_DOWNLOADS, "download"); 
                    DownloadManager dm = (DownloadManager) getSystemService(DOWNLOAD_SERVICE);
                    dm.enqueue(request);        

        }
    });

Option 2 ->

if(mWebview.getUrl().contains(".mp3") {
 Request request = new Request(
                        Uri.parse(url));
                request.allowScanningByMediaScanner();
                request.setNotificationVisibility(DownloadManager.Request.VISIBILITY_VISIBLE_NOTIFY_COMPLETED);
                request.setDestinationInExternalPublicDir(Environment.DIRECTORY_DOWNLOADS, "download"); 
// You can change the name of the downloads, by changing "download" to everything you want, such as the mWebview title...
                DownloadManager dm = (DownloadManager) getSystemService(DOWNLOAD_SERVICE);
                dm.enqueue(request);        

    }