The limits of power of the ICO are to issue fines. However they are highly respected and their influence huge. They are a very powerful body.
If they came out with a highly damning report (they do lengthy explanations point by point of their findings and each point of failure with references to attitude and culture of the organisation) it would be difficult for other public bodies to ignore. This is the important bit really, rather than the size of the fine.
The ICO reports directly to parliament (under the Department for Digital, Culture, Media and Sport), thus if their concerns were serious enough, this carries significant weight with other government departments.
Anyone who answers to another government department would have some serious questions to ask if they were involved with this charity because there would be concerns over the charities attitude and ability to govern itself full stop. This naturally would invite a lot more scrunity than Mermaids have been used to. Would they survive this in their current form?
On a corporate level would you want to go near a charity with a shitty reputation, if you are looking to virtue signal? Would you give a charity which had demonstrated poor governance a big grant? This could restrict their income to just personal donations. And if you've heard a scandal about a charity and they've had a big fine would you want your money to go to that charity?
Their whole reputation and brand is now under the spotlight by an organisation which hasn't been inflitrated by a load of people with a woke agenda. Their interest is purely to protect people on a data level.