You seem to have quiet a rosy view of the British class system, but that is not the reality. Money or profession will not just make you higher class here in UK.
Maybe the term that I was looking for was middle class, rather than higher class. I'm just comparing it to Hinduism, where a lowest caste dalit cannot even progress to middle castes even if he becomes a billionaire.
Perhaps you are mixing up “class” with “caste”? Because it’s perfectly possible for a poor lower caste person to climb up the ladder of “class” to be a middle class. It does buy you certain privilege which otherwise wouldn’t be possible. Because money, ad the end of the day, does matter to an extent.
Caste on the other hand is an entirely different beast, as you have rightly pointed out.