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It was a long time ago but I'm pretty sure that I just painted over the top, having first wiped it down with some sort of degreasant. The drawer interiors remain in their original colour.
ETA - they've been kind of OK over the last 35 years - with minimal chippage. How much work do you want to make for yourself?
ETFA - I tend to go for the 'What's the minimum I can get away with to make this stuff work?' approach
I have some of those.
Hammerite was my friend.