Blueberry pest

This is my first year growing blueberries. They are in half barrel sized plastic pots in ericaceous compost on the allotment and have flowered well and are now getting berries. I left them without netting so they could be pollinated.  In the last few weeks I noticed that one of them in particular was being eaten (its leaves) by something and I thought it was slugs so put pellets around them. Today I realised the culprit is actually thin grey/black furry caterpillars and they are stripping the leaves. Does anyone know what this moth/butterfly might be and how I might avoid it? If I net them when they're flowering, how will they be pollinated?