A lot of the confusion arises with these wheels & centres because they have been made by a good few different people over the years.
They were first designed by John Thornton here in Leeds (about 1/2 a mile from where I am sitting typing this) in around 1967. John had made a minor name for himself hereabouts after designing his Mamba Single seater.
Following this success he decided to design an alloy wheel that was above all light, but that could also be easily converted to a whole range of different rim widths. The result was the Mamba Alloy Racing Wheel. This was available off the shelf in 5 & 6 inch & was available in rim widths up to 10" (or even larger) to order. The rims were initially cast up in a Leeds foundry & finished by John. These very early Mambas can be seen on cars like Alan Staniforth's Terrapin.
John sold the project to a Foundry in Halifax in the early 1970's who manufactured the Mamba wheel in standard sizes until the mid 1980's. When they closed down.
Since then there have been at least another couple of people who have offered this design of wheel either with, or more likely without actually holding the manufacturing rights to do so.
As far as I am aware the only company still manufacturing this style of wheel is JBW who are having them made in the far east.
Throughout its life, the wheel has had a number of different centre caps, the most common is the straight domed type in 360's post above. The "mushroom type" that Goff has shown pictures of is of an earlier design & is MUCH rarer. The original designs were always pad or screen printed on, but Goff's stickers look pretty much perfect to my eye.
I am not aware of the original John Thornton Mambas coming with a centre cap of any sort.