Local folk music publications are not normally taken as advertising (at least for the current restrictions on advertising members only clubs). If that wasn't the case then a lot of magazines wouldn't have any listings.

Any mention in a more general publication is regarded as advertising, even if it appears without the knowledge or consent or the organiser. Islington Folk Club (members only) came very close to being closed down a year or so back because a guest sent a press release direct to Time Out.

So if your local paper does pub reviews and your session gets mentioned in the pub's write up then the music will cease to be incidental!