Feeding the birds?

We bought this bird feeder a few days ago.  The wire cage around the feeder is supposed to keep out the big birds like pigeons and crows.  We also thought it was designed to keep out squirrels. 

As you can see from the damage, it isn't very successful at the latter.

Squirrels are very cute, but I don't actually think they need our bird food to thrive - we would prefer them to leave the food for the finches and tits.