However, there is a way to achieve this. Simply hold the power button down for a few seconds as if you were powering down the phone. At the bottom of the popup dialog box that appears there are 3 options.
The left option will mute all sounds without vibrating, the middle will vibrate instead of playing sounds and the right will make the phone play sounds as per your volume settings.
You will need to return to this popup dialog to turn off this setting as your normal volume settings are ignored while muted.