Well there's your real fake news.
I'm sure it's not the first or last entirely manufactured and completely outrageous story. No one can know unless they have the time to research every damn story a paper runs.
It's reminiscent of The Sun in the 1980s, when they ran with the idea of the "the story too good to check," which -- back before people became aware of this stunt -- involved phoning up a "loony left London council" like Haringey or Lambeth to ask for their reaction to something they claimed to have heard the council was doing, like banning black bin bags on the grounds they were racist (an actual example).
Back before people realised what was going on, more often than not the call would be taken by some luckless person in the council's refuse collection department who, not having heard anything about this, would assume it was some official policy she'd not heard about and try to improvise a response, which the paper would then print as a defence of a policy that didn't actually exist, along with outraged comments from right-wing MPs who had been asked by The Sun to comment on the improvised defence of a non--existent policy, and thus the controversy over racist bin bags (or whatever it was this week) would begin.
This carried on until Haringey (I lived there at the time, and was a member of the local Labour Party, which is why I remember all this) introduced the policy -- standard now, of course -- of telling staff not to respond to press inquiries at all but, instead, to refer them to the council's Press Office, and making it known that any paper printing this kind of fake story would automatically be sued for libel.
That put a stop to the practice, but this seems to be a contemporary equivalent -- in this case, the Times and Mail didn't need to check with the RNLI, but simply took the information out of that organisation's annual financial report and asked a couple of their tame but over-excitable rent-a-quote Tory MPs to fulminate about it.