The first Folk Club that I ever attended was in my home town of Peterborough, around 1967.
The club was in the back room of a pub (which, sadly, is long since demolished). The evening started around 7:00 or 8:00 pm (can't remember which now). Attendees paid a nominal fee at the door. There may have been seats around three sides of the room (although my memory may be faulty here) and there were pub tables scattered through the room, each with 2 or 3 chairs - you sat wherever you could find a seat. At the end of the room, furthest from the door, was a raised stage (I think!).
There were around 4 or 5 resident singers: these were a varied bunch - one was a (white) blues singer, one sang mainly comic songs, many of his own composition, a man and wife duo did mainly American songs and chorus type songs and another sang English traditional songs. These residents took turns to fill the first part of the evening, doing about 2 songs each.
Next up was the 'Guest'. This was usually a professional, or semi-professional, singer booked in advance by the club organiser (who was also one of the residents). The Guest would entertain us for the next 30 - 45 minutes and then there would be a 'beer break'. After that there would be a chance for 'floor singers' to have a go (ie. members of the audience with a desire to participate, visitors from other clubs or even semi-professionals angling for a booking).
The evening would end with another session from the Guest who, of course would be thanked effusively by the club organiser, subjected to thunderous applause by the audience and urged to perform an encore.

Amazingly, all of the clubs that I have attended since, in a number of different parts of the country, have, with minor variations, followed much the same format.

The other important thing about UK folk clubs is that they are often very friendly places and can be very good from a social point of view. I have made many good friends, over the years, and consider myself very lucky to have encountered such a wonderful institution.