Sonos Radio plays only through the SONOS players.

My problem is that when I disconnect my mobile from wifi, the speakers dont play music

SONOS is normally directly connected to the Internet and you can think of the phone as a simple remote control. Once music starts to play, the phone can be turned OFF.  This Internet connection could be through a wired Internet connection or WiFi. 

Another mode is using AirPlay to send music from your phone to the SONOS system. In this mode, the phone must be powered and using the same WiFi network as the SONOS system.

SONOS Radio cannot use AirPlay.

So the speakers can play Sonos radio when connected to WIFI without the need of my mobile existing in the same WIFI. 

My example is that i have placed the 3 speakers at office and I want to play during work without the need of my mobile.

Which radio service have you added to the work system? As @buzz already said, the phone/app is really just a remote control for the speakers so once you’ve issued the “play station x on service y” instruction, the music streams from internet/wifi and the phone becomes redundant. 

Thx all for your responses

I play Smooth fm from SONOR radio. 

So I understand that the disconnections i have come from WIFI issues. Probably is the firewall cause the speakers are at company’s offices