I would argue that it still hasn't completely. The UK is still very much a hereditary class-based society, and people from traditionally middle-to-upper class backgrounds tend to do much better in life than people from traditional working class backgrounds. One of the Chambers of Parliament, the House of Lords, is only made up of unelected peers, many (if not most) of whom are of aristocratic lineage (and around 10% of positions are actually hereditary), and while the House of Lords may not be as powerful as the elected House of Commons, it still has the power to block new laws from coming into force. Not to mention the fact that the current Prime Minister went to Eton (as did much of his cabinet) and is distantly related to the Queen.