The stilted phrasing in the report from Salmon Business definitely does not sound very credible, but marine life protection is definitely a real thing with nuclear and all fuel-burning electricity generation
The vast quantities of water needed to cool nuclear (for every kWh of electricity, 2 kWh of waste heat must be discarded) can have significant impacts on wildlife. In the past, we just devastated ecosystems but most modern countries decided they didn't want to do that anymore.
This is not a nuclear regulation, it's a "thermal plant" regulation, it's just that nuclear needs more cooling than, say, combined-cycle gas because nuclear's lower temperatures are less efficient at converting heat to electricity.
At a mere $700M, even dropping all marine life mitigations from Hinkley Point C wouldn't help much with affordability. If they could drop $7B of costs from Hinkley then it may start to have a halfway-competitive price, but it still wouldn't be very attractive.