While the South Sea Company and its collapse is a relatively obscure topic today, that's not to say it didn't have consequences. In order to deal with the economic crisis caused by the company's collapse, George I called on Robert Walpole to manage the emergency. A year later, the king appointed Walpole First Lord of the Treasury, Chancellor of the Exchequer, and Leader of the House of Commons. This made Walpole the most powerful minister in the government, and demonstrated how a high-ranking minister could be the actual head of government. Because of this, Walpole has been retroactively labeled the first Prime Minister of the United Kingdom, even though he never actually used the title.
Suppose there was no South Sea Company, and so Walpole never became as powerful as he did IOTL. What effects would this have?