Bird feeding with rats in the garden

Does anyone have any suggestions on how I can still feed the birds this winter when I have found it encourages rats in my garden? They seem to be able to climb up and still get feed from feeders which are supposed to be vermin proof . Also there is still spillage by the birds which encourages the rats too.
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Apparently the rat population has exploded this year, it's been mild.
Do you live in a city @Fallon?, I think the rat situation is worse there.
I nearly took my finger off this morning trying to bait a 'killer' trap - oops!! Don't think I'll use that one again, far too dangerous for someone who's a bit accident prone.