Jaeger, some clubs will require them, others won't.
Swinley, for instance is jacket mandatory, tie optional.
Deal is golf shirts in the main bar, jacket and tie in the lounge and dining room.
In many, a post round beer, sandwich etc can be had in golf clothes, but proper dining means jacket and tie.
Also worth considering is clubs requiring "long hose" (ie. knee-socks) to be worm with shorts.