I fully endorse what you say Cluin,Gulliver and Scrump.
I guess it all depends on WHY the musicians/singers are in a pub/club in the first place.
If they are a small clique of folkie friends/associates who just want to get together to have a "Pivate" acoustic session then,with the agreement of the landlord/lady,they should hole up in a secluded room well away from the main bar area and just entertain themselves.

If,however they are there at the behest of the owner/landlord as an attraction/treat for his clientelle they should perhaps be centre stage in the main bar or in a room big enough for the musicians/singers AND interested/participating members of the 'public'.
This will only work though if the 'folk session' includes a generous amount of "the more boring standards"(Cluin)which are well known chorus songs that joe public will want to tap his foot to and maybe even join in with. So every one has a good time,drinks lots of beer (So the landlord is also happy!)and go away to tell friends and family what a great time they had.
Actually I don't agree that the standard favourites are boring. These are the ones that an 'audience' will expect and want to hear.
You can always interject some of the more obscure and throat-cutting tunes/songs but leave the standard favourites out at your peril.
As Cluin says this makes you more welcome to the venue and clientele
and also very importantly it shows that you are welcoming and happy to encourage others to learn songs and join in.
If you 'exclude' people it is then that you will have a battle with the background din of disinterested people,TVs,juke boxes and any other form of sabotage that you most probably deserve.
Folk sessions and the folk tradition as a whole was never intended to be a 'private' party turning its back on and excluding the majority. Is for everyone and the more people that are encouraged to play,sing,or just join in with the folk fraternity,the better.

Shaneo, I don't know if the place you walked out of invited you to have a session there or not and I agree that "most pubs will show respect for the musicians and switch off the TV etc" BUT ONLY IF:
* You are welcome/invited by the ownwer/landlord and have checked your position with any new owners.
*You manage to keep the clientele interested and don't just have endless 'twiddley dee' of just musicians for hours on end because joe public will soon lose interest and attention and ask for the TV to be turned up.
*You therefore break up the session to include playing/singing those very traditional and popular songs that (most) people want to hear.
*You spend some money at the bar.
People will most definately turn their backs on real/live music if it 'all sounds the same'(musical wallpaper),has become boring and so they have lost all interest.

If the pub/club venue is not flexible and you are not flexible it isn't going to work. You can't just engage in battle and play/sing louder to compete with TV,chatter,juke box etc.
The only thing you can do is pack up your instruments and voices and seek out a new venue where hopefully it will work out to everyones advantage.
But whilst packing up your instruments sometimes it might be worth asking:
-What went wrong?
-Were we actually welcome there in the first place?
-Did we engage and involve the public/clientele?
-Why did they lose interest?
-How could we change things and be more flexible in our approach so we are less exclusive/private?
-Has it been worthwhile to the owner/landlord in terms of increased custom from customers?
-Did we spend much money over the bar or are we still labelled as "they don't drink enough" brigade?
-Is there a better location in the pub where if we are not wanted by the pubs customers we can be less intrusive and away from TVs etc.

I am sorry that you had a bad experience Shaneo and wish you every good luck and good hunting in your search.