Speaking as an American who thought he knew a lot about British culture, I am surprised, chagrined, and annoyed to see that there are a couple of items on the original list I have never heard of:

The Angel of the North

SS Empire Windrush

The "Routemaster" Bus – well, I suppose I've ridden them, but I didn't know they were called that. I would have just called it a "double-decker bus."

Here are some things I consider icons of Britishness:

The "hackney carriage" a.k.a. "black cab"

Stilton cheese (followed by double Gloucester, Wensleydale, and red Leicester). Perhaps Brits would like to claim cheddar as their national cheese, but it is too common in America for us to consider it particularly British.

The pillar post box.

The Tower of London

The works of William Shakespeare

The Rolls-Royce (followed by the Jaguar, the Triumph, the Morris Mini, the Land Rover)

Parliament (I mean the institution, not the building, although the building is distinctive, too)

Marmite

The waxed jacket, flat cap, and green wellies

The Foot Guards

* * *
By the way, I'm guessing the compilers of the original list wanted to include only one item in each category. Stonehenge fills the category "building", so they had to omit the Houses of Parliament, Westminster Abbey, etc. The King James Bible fills the category of "serious literature", so they omitted the works of William Shakespeare, and so on. I see they also have one work of children's literature, one sculpture, one painting, one ship, one airplane, one land vehicle, one song, and one drink.

That rule probably accounts for the omission of most of the things we have been mentioning here.