You could always try suspending one of those shiny wind-spinner type things underneath the basket, or hang it somewhere on the bracket behind the basket. Apparently birds don't like shiny things (unless they are magpies!), and this keeps them away. You could also try strips of tinfoil, or old tinfoil tart cases suspended between the baskets. This is what I'll be trying when my strawberry runners eventually arrive.
Amazing what you can learn by being forced to watch CBeebies by your despotic sproglets!