A "foul and a miss" is exactly what it says....the player played his stroke and "missed" making initial contact with the ball on. In your case, your opponent certainly made initial contact with the ball on therefore, the proper call is "foul, four away" (or whatever point value required), ball in hand for the in off and standard options (play the next shot yourself, or give it back to the fouling striker).
About an earlier post you had regarding inconsistency in how the "miss" rule is applied:
In my club, we have a simple rule of thumb as to whether the "miss" can be called. If, prior to the stroke, the striker can "see" any part of any ball that is on or could be on in a straight line of contact (does not require swerve or off cushion), then a "foul and a miss" will be called if he does not make contact. This applies even if the striker DECIDES to play off cushion when he could have chosen a different, straight line shot (for instance, on colour, white is buried in pack of reds, can SEE the black but chooses to play off cushion to a baulk colour--foul and a miss). If the white is fully snookered so the striker has no choice but to swerve or play off cushion then "foul and a miss" will not be called by the opponent. However, some of us are higher caliber players (though still not all that good) and actually enjoy playing the game using the miss rule as written so that a player is allowed to call a "miss" on himself if it was a full snooker, even though the opponent cannot call the "miss". Initially, this probably sounds odd, calling "miss" on oneself, but it is certainly not without precedent....players call fouls on themselves all the time in case the referee was not in a position to actually see the foul. Snooker remains a gentlemen's game--if a player commits a "foul and a miss", undoubtedly the player knows he committed a "foul and a miss" and so he should be ready and willing to call it.
Prior to implementing this, we also had some arguments and tense situations on the subject. Some of the players desire to have the highest score to win the frame no matter the method of arriving, even if it means fluking a great snooker and charging ten "foul and a miss" penalties. Others, like myself, consider this to be bad snooker and enjoy the full flavour of the game in the spirit it was intended to be played. For me, the spirit of the rule is that if the striker makes his best honest effort to make contact with the ball on, then there simply is no "foul and a miss" even if he misses contact by a foot or more...the striker himself is the only one who knows his own mind so he is the only one qualified to determine if he truly made his best effort or not. Those of us who call a "miss" on ourselves are doing so because we want to improve our games overall, and better learn the angles around the cushions by learning from our mistakes.
This only applies to non-refereed frames which is basically all of them over here in the USA. I believe in the UK, you guys often have enough interested players that your league games can have an actual referee so the problem is that he has to "read the mind" of the striker. It is easy to read the mind of a professional because we all know how good he is, we know that he can get out of that snooker if he makes his best effort. But "normal" players may be trapped in a relatively easy to escape snooker, make their best analysis of the cushions, strike the ball at dead weight and still miss contact by a long way. By proper interpretation of the rule, this should not be called foul and a miss but some other knucklehead snooker player acting as the referee may well call it a miss because he thinks that contact was easy to make. So my humble opinion is that your acting referees should not be calling misses like this unless it is painfully, clearly obvious that the striker committed a deliberate foul. So what is "painfully, clearly" deliberate? If the player "accidentally" miscues and squibs the cue ball when snookered; foul and a miss. If the player has to go off one cushion three feet away to strike the object ball another 9 feet away and the cue ball barely bounces off the cushion a foot or two; foul and a miss. Same shot, he comes up six inches or a foot short of the intended object ball and/or three or six inches to one side; not a foul and a miss. Etc., etc.