Actively blocking cell phone signals might be illegal depending on your country - but building a faraday cage isn't.
Given how much of your identity a phone has become, and how easily someone could take my identity over if they had access to my device, only death or threat of deadly force will separate me from mine. If you want to go for the "handing in" approach, maybe small lockers are ok (especially so if they are padlock-operated and I bring my own padlock). Bonus points for being able to charge the battery in these (Like the phone charging boxes often present at airports)
In Europe, there are several places that offer "connectionfree vacations", often in remote valleys, often in monasteries (sometimes run by clergy, sometimes not) with thick walls.
Such a "cell" would be best if it not only had a desk, but also something more comfortable, like a couch. Bonus points for the ability to get cold and/or hot beverages on-site.
I'd pay a monthly membership fee of around 50 Euros for this.