But the United States is directly and pervasively the child of the British Empire. Its institutions, legends, history, culture, language, beliefs, and mindset are all Britain's -- the US is a successor to Britain. Which is obvious, of course, because it was a British colony -- so there's no surprise there.
The difference lies in the institutional continuity. While William the Conqueror may have thought of Rome as some mythical and grandiose concept (or maybe not), even he, at the beginning of 'England', was 1000 years out from the heyday of the Roman Empire.
The US, by contrast, was directly moulded by the heyday of the British Empire, which I would say extends from 1815 to 1945, whence it ceased to be a superpower, and America took up the gauntlet. It was a direct successor and in fact continues close relations to this day.
Ancient England's relationship to Rome was nothing of the sort.
Wikipedia seems to think that, as Kahn and Cerf both directly say, they had a part in its creation, but it wasn't their invention -- in fact, it was many peoples', because it's not something that can actually BE invented.
However, networked computers CAN be invented, and a Briton did it -- Donald Davies..
The modern format of the Internet, the ubiquitous and universal World Wide Web was invented by Tim Berners-Lee, another Briton.