Refurbishing badly painted, rusty radiator
I have used a wire-wheel on an electric drill to remove loose paint and rust from a radiator. It can be hard work but you can get down to bright clean steel using those tools. Your case looks extreme but I would try that to judge the effectiveness.

I would aim to remove all traces of rust. If there is too much rust for this to be practical, that might be a sign that it would be better to replace the radiator.

I note that many "Hammerite" products are designed to be painted onto rusty surfaces - I'd check the information on the tin. 

I used aerosol cans of radiator primer and top-coat.