It has nothing to do with cost of living; it’s market rates which are set by supply and demand. London is super expensive but the pay is much lower than even the rural American pay scale since UK engineers don’t get paid well anywhere and will work for Google even if they’re getting half of what they’d get in the US. They could move to the US—Google would support the transfer—but they don’t, so there remains a supply of people who are willing to work for that rate in London.

As others mentioned, if Google ignored supply and demand and paid for quality of work only, why would they pay everyone the high rates that were originally set by supply and demand in Silicon Valley? They’d pay a normal living wage for someone in India.