There is a steel container full of control gear where I work, I can easily make mobile calls from within it, even with the door closed.
This being the case a spy device using microwave freq's would also work.
The container is about 2mm steel, so you either need to use steel much thicker or something more conductive like ally or copper.
You can use mesh, the size of the holes is depicted by the highest freq you want to block, for phone signals I'd take a guess at 3mm or less holes.
Copper cable is sometimes sold as copper when actually its copper plated ally, you can tell by weight.
If you have no experience of electronics dont try to build a jammer for all frequencies, such a device is a challenge for an experienced engineer.
I'm sure the device you linked us too does what it says, however spy devices can use other freq than phones, to block lower freq signals would require a huge antenna.