That was the prediction. But ultimately no correlation was found.

Source: Mahaffey, "Atomic Accidents: A History of Nuclear Meltdowns and Disasters"

This is assuming the LNT (linear no threshold) model of radiation damage is true. Which it probably isn't. Lower than predicted deaths from accidents such as Windscale/Sellafield are sometimes taken as arguments against LNT.

However, in all such discussions, one needs to be aware of the strong interest of the British government to keep all things around it's nuclear weapons program secret. So maybe the public figures are fake.

Few things in medicine are linear. DNA has error-correcting codes, much like a hard drive or network connection.

In hard drives or networks, errors are tolerable below a certain threshold. It's a different story once unrecoverable errors start to occur (data loss, system crashes, perhaps errors getting caught by higher-level things like exceptions).

I'd expect DNA, cells and biological systems are probably similar. The error correcting mechanisms can probably handle some errors up to a threshold (which probably itself varies between individuals).