The correct primer for painting a galvanized surface is "Calcium Plumbate". It's available at some DIY outlets as I have seen it.
I live near Droitwich and the DIY place "Wigleys" near Stourport used to have it on their shelves.
How do I know about this primer??
Well, I used to work at a steel fabricators/ erectors and Dave , the boss, would take on anything.
The Severn bridge taking the M50 over the river was galvanized steel and when first erected it was just painted over.
The paint came off "in sheets" he said. So he took on the job of stripping and repainting said bridge.
Calcium plumbate was the primer specified for the job.