Once it is downloaded it should give you the option of restarting your laptop to finish the update. Do you do that.
Are you letting Windows Update download updates automatically if so try downloading them manually then restart the laptop.
Take it you have lots of room left on your hard drive..
Try using disk clean up and when that is finished running click on clean up file system on the new box that opens. That should remove any old updates and I would do that before checking for new updates.
Or. Control panel. Troubleshooting, Then click on the windows updates and run that to see if it finds any problems.