I agree with Bert, and it really does work. I used always to sing loudly (I am a noisy female with a very powerful chest voice), but was amazed when someone told me you don't have to be loud all the time - and he proceeded to sing a song fairly quietly. When he sang quietly the general noise level went right down. When I sang loudly the general noise level went up. Its logical really - if there's loud music on you have to talk louder to be heard.
As Alice says, training doesn't make you into an opera-style singer. Training does teach you to make best use of your voice without damaging it. I'm having to unlearn the blasting-out-loud stuff and learn to use more control at a lower volume - so its not just quiet singers that are helped by going to a teacher!
Its definitely worth going to a teacher at least for an assessment, and if you find a good teacher then keep going! If the pub just won't quieten down (and some won't) then just accept that its not worth trying to sing there, and find a quieter session to sing at. There's no shame in deciding its not worthwhile. Quiet a lot of our best local singers simply will not sing in a noisy environment.
Is there any mileage in doubling up with someone else for a song or two - does two quiets equal one loud?
Keep singing anway, even if not at that venue.

Kris