The ANO is very badly drafted, as is much UK legislation. My interpretation of what it means (as a law professor) is that no information or advertising about this particular flight can be published (with the flying club exception).
The obvious way to proceed is to give details of past flights, explaining how much they cost. This can't be seen as advertising of a future flight. If your friends and acquaintances then want to arrange a future flight with you, this gives them some idea of costs but won't infringe.
What won't work is: "I'm flying to X next Saturday, anyone want to share the trip and costs". This is unlawful, outside the club environment, even if you don't calculate the costs up front.
The purpose of the law is to prevent you running something that is like a passenger service, with the schedule set out in advance. Read the ANO with this in mind.
Sophistry about websites being premises, or a closed group of (passenger) friends being a flying club, is not worth bothering with. I looked into this type of approach when advising on an internet lottery in 1995, and took the view that no court was likely to be impressed!
As always, this is a general analysis and not advice about your website (which I haven't seen). Plus, my opinion is worth precisely what you paid for it.