I think skyhigh has a point here: we do seem rather reticent in the UK to use the radio (from the POV of the pilots) to actually organise circuit traffic.
Sometimes I think people come into conflict because even if they see one developing, they can’t think of the right phrase from CAP 413 to defuse the situation, so end up doing a last-minute manoeuvre or complaining to all and sundry well after the incident.
If I heard “Joining finals for XX” and there were five aircraft in the circuit, including one on base leg, I’d say something like “it might be a good idea to do an overhead join as it’s very busy” or “you are number six to land, BTW” or if I felt really snarky, “negative Ghostrider, the pattern is full”.
Equally I could say something like “there’s one on base leg but quite a gap between him and me, I’ll extend and come in behind” or something neighbourly like that.
I prefer to think that very few (if any) pilots
deliberately cut other people up, just that their situational awareness is not as good as they think it is. Just look at all the airproxes that could have been averted just by passing a bit more information...