Or you could alsways start Fair Trading proceedings…
If it is unequivocally a failure to maintain the common property, then yes. Branches contacting the building would be but the other aspects of the complaint perhaps not.
Some owners might prefer to let the trees grow to provide more shade or privacy or whatever, while others might prefer form pruning to let in more light and retain a view. If it is a difference of preference about how to maintain, then a general meeting vote might be more appropriate to make that decision.