Great spotted woodpecker

On the way to dropping our daughter off to school we heard a woodpecker drumming on a tree truck. I kept an eye out on the way back and noticed a woodpecker flying into the same trees (at the back of Emmaus) opposite Easthill Park (Portslade). Almost straight away the woodpecker started to drum on the trunk at the top of an old tree. This was a male great spotted woodpecker, recognisable by the red patch at the nape (back) of its neck. After about 5 minutes another great spotted woodpecker arrived in the neighbouring tree. This was a female (no red nape). Then a third woodpecker arrived and the female made what sounded like a warning call and looked agitated. This is the first time I have seen three together. After a couple of minutes she chased off the third woodpecker (could not see if this was male or female - possibly female and was considered a rival?). After another few minutes the original woodpecker flew off in the same direction, south west over to trees on the far side of the horse sanctuary.