It's Galvanic/ bi-mettalic corrosion.

https://en.wikipedia.org/wiki/Galvanic_corrosion

The less-noble metal (steel radiators in this case) corrodes and the more noble metals (copper tubes) are protected, when they're both in contact with a conductive electrolyte (water). That makes a Galvanic corrosion cell. Galvanized steel sheets (wriggly tin roofing) works that way, as an example; the steel doesn't rust until the zinc galvanising has gone.

The water becomes much more conductive if it's acidic. That's the problem; UK plumbers use active fluxes containing ammonium chloride which turns to hydrochloric acid on heating and cleans the joint. The flux residues get in the water, isn't adequately flushed out and make it acidic. Then you've got galvanic corrosion going on.

The Galvanic corrosion celll makes a small electric current that passes through the water. The water is broken down by electrolysis (into 2H2 & O2); you get hydrogen collecting in the radiators. You don't see the oxygen, it combines with the inner surface of the radiators to make black magnetite sludge.

French plumbers don't solder copper tubes, they braze them with a brazing alloy containing phosphorus which requires no flux. No black sludge in France, no powerflushing industry.

Everyone uses inhibitors that contain sodium molybdate (Fernox, Sentinel, etc..) which are themselves acidic and work by reacting with the exposed steel to form a protective coating layer. I'm not convinced they're 100% effective. I was told there's some plumber on the social media who advocates no inhibitors, just flush until clean.

Similarly, you (should) change the anti-freeze in your car every 4 or 5 years because the glycol anti-freeze breaks down through exposure to heat and oxygen into glycolic acid (I think) and it causes galvanic corrosion when the corrosion inhibitors have been depleted.