Englishal - you are right, both aircraft should have heard one another on RT, but, Shoreham does not have radar. They probably rely solely upon pilot information.
If for example, aircraft A calls up for departure, for a standard circuit and whilst accelerating in the roll hears aircraft B call up "letting down deadside for rejoin" Aircraft A for sure would be looking out for aircraft B.
Once aircraft A has reached 500ft he would then turn left still ascending onto crosswind still looking out to his left for aircraft B "joining" crosswind.
Why would aircraft A be looking directly behind in the climb on crosswind. One doesn't expect a prop chomping away at your *rse from behind.
When I call downwind and another aircraft calls finals, the picture that I am expecting is the other aircraft to be in front of me, having completed base leg and descending on the runway heading, but after this discussion I will now be looking everywhere for that traffic.