It is very difficult to bring down a drone without the potential for collateral damage. The one that is being used looks like it is one of the £5k professional ones. They can survive some damage and some can even compensate for losing a blade.
Shooting it with a rifle is next to impossible (drone is too erratic and where will the bullet finish?).
Shotgun (drone is too high). It's legally limited to 400feet, but it would appear that he is being a bad boy and flouting that law. My drone can climb to nearly 5000feet
Jamming the signal. Drones normally work at 2.4GHz and so does WiFi. Also, there is danger if it just drops from the sky.
I did see some software that can identify the exact frequency the drone is using and target the transmitter. I'm not sure why this isn't being used. Perhaps it doesn't work in the real world.