A Mode S transponder does not provide the traffic avoidance function per se, but is a necessary component of a complete ACAS II system. 2 aircraft with Mode S transponders, but no ACAS system will have no more direct protection from each other than aircraft with Mode A/C or no transponder. If one of the aircraft has an ACAS II system, it can generate a collision-avoiding Resolution Advisory for it's crew to follow. If both aircraft have an ACAS II system, the RA is co-ordinated by communciation between the 2 ACAS processors through the Mode S transponders.
The RA action is only the vertical plane; the azimuth information is much less reliable and is presented to aid visual aquistion rather than to cue lateral avoidance. Contrary to what has been posted, the system works below safety altitude, and can issue a "Descend" advisory depending on radio altitude. The radalt input disables the RA function automatically when close to the ground for take-off and landing.
PH-UKU,
Your Mode S transponder has been mandated by EASA, citing that it is essential for the effectiveness of ACAS on commercial air traffic. As BBD has described, the ACAS II system takes equally effective unilateral action against an "intruder" with either a Mode S or a basic Mode C transponder. I suspect that Mode S, rather than just Mode C, has been mandated because of the additional benefits of the Mode S Elementary Surveillance (ELS) function to ATC.
I don't think that any of the RAF fast-jets have an ACAS system. The Tucano has a form of ACAS I (no RA information) but the Herc does have a TCAS (I think), so keep squawking and heed all the old advice about lookout.