Blackcaps bullying other birds away

Help please! I have been feeding birds for about 2 years and have built up a steady 'clientele' comprising robins blue/great/coal tits, blackbirds, starlings, wood pigeons, sparrow, occasional dunnocks, wren and sometimes even a woodpecker. But this has all changed since the arrival of black caps about a month ago. At first it was one, now it's at least two different ones. Initially quite polite and unassuming, i actually felt a bit sorry for them as the Robin was bullying them and now they have turned into the worst bullies themselves! The sit in branches for ages and swoop down to chase away any birds approaching the feeders, especially the tits and the sparrows, who at least fight back as there are many of them. I normally replace fatballs every day or every 2 days and now haven't replaced them in 10 days! Does anyone have any tips? I am unable to move the feeders around as I don't have any other places to put them.