Cigarettes were not rationed during World War Two, presumably to keep up morale, and numerous brands were available - at least in theory. In practice the shortages and austerity of the war years and the years afterwards meant that specific brands did not always find their way to tobacconists or cigarette vending machines. As often as not shops were completely out of stock of cigarettes or kept them 'under the counter' for regular customers only.
My main recollections come from after the war, when my father was back at home. He smoked Players Navy cut which was a common brand, but there were quite a number of other brands, all well advertised and popular. The photo gives a good indication of the range.
My father taught me how to make a bookmark from the Players packets by cutting round the outside of the life-belt and most of the way round the inside. This made a flap which slipped over a page and did not get knocked off or slip out. More recently I have made such bookmarks from cereal packs, which are made of the same thickness of card, but the pictures are nowhere near as pleasing and not really the best size.
Cigarette cards which were common before the war never really took off afterwards, although I understand that some cigarette brands produced a few to mark special events like the 1951 Festival of Britain.