I was just curious, is there a link or is it just coincidence because they sound so similar? If so, do you think that the Imperials are inspired by the British Empire (and Romans too) (I'm new to this forum, hello!) :')

It seems you're familiar with the East India Company, so you'll know that the company was just as much a governing body as it was a commercial enterprise. From what I've seen, the East Empire Company is just a group of Imperial traders pursuing economic interests in Skyrim, with very little ties to the Imperial forces that help administer the province.

Seeing as they both seek (or in the case of east india; seeked) to monopolize trade in their respective regions, and do so with some government support, I would say so. It is true they are not involved in local politics in elder scrolls, whereas they controlled Indian governmental policy. Still the similarities are there.

Imperials in Elder Scrolls act ( and obviously dress) more like the Romans than the Colonizing British.

The Romans often left conquered municipal governments in place, or replaced them with puppets made up of Roman sympathizing natives of that specific region, so that they remained semi-autonomous.