What is knocking upon the breast and when does one do so during mass? I do not believe I have ever seen anyone do it (although if you don't know what it looks like it may be hard to tell.) Do any of you do so in your parish?
It is a manual act said in the course of the consecration prayers. A fist is made and you smite your own breast lightly (or really hard if you want to, I guess) at the words, "And although we are unworthy. . ." I don't have a '79 BCP close to hand but I would not be surprised to find that the phrase was discontinued in most of the Communion rites. Anglo-Catholics who use the Missal may also insert the gesture in another place, I think the prayer of general confession but I don't regularly use that rite so I don't keep up with the peculiarities of its practice. But one of my fellow priests smites his breast thrice during the General Confession.
I have seen it done in Catholic churches when the "Confiteor" is used: https://en.wikipedia.org/wiki/Confiteor
The Prayer of Confession in the Communion service (Anglican Standard Rite) of the 2019 Prayer Book has this phraseology: "Have mercy upon us. Have mercy upon us, most merciful Father." The three-fold 'mercy' is not unlike the old Roman confiteor, and so I usually 'beat my breast' at that point. I doubt anyone else can see or hear it, but that isn't the point
In our Anglican Catholic Church we use the small pew Missal and in it is our order of service. The act you speak of is done during the Agnus Dei, before the Prayer of Humble Access.