What classical Hinduism had was the
varna system, where you were a member of a particular
varna according your jobs and qualifications (for eg, bhramans were supposed to be learners and teachers of scriptures, analogous to professors and phd's today). And even this
varna system was debated and discusses throughout classical Hinduism, as with every other idea in Hinduism was.
But overtime, especially when people of different cultures and languages interact, things can become twisted and lost in incorrect translations, whether through genuine error,any inherent biases of the translator or malicious intent.
And also overtime, cultures can evolve in response or in interactions with outside forces (especially the Islamic and later European invaders over a 1000 year period) that would seek to implement their own hierarchies and systems. Infact, the indigenous Indians were treated as second class citizens in empires established by outside invaders (Jaziya collection is common example of this).
But what generally makes the system as being attributed to the British is due to the Divide and Conquer strategy implemented by the British. Dividing the populace becomes a lot easier if you can mutate or deepen existing lines in the system.
But truthfully, the exact lineage is very hard to find, especially for a culture that is not only 5000+ years old but has also been interacting with and assimilating just about every other global culture during that 5000 years period (Indians have been interacting with everyone from Chinese, SE Asians, Romans, Greeks, Persians, Mesopotomians, Africans, Arabs, Ancient Egyptians, Turkic Nomads, etc)