It is easier to become a millionaire in the USA but it comes with some obvious risks. In this, it is easier to become ultra-rich in the USA but also easier to fall into utter destitution.
First, the Gini coefficient or a number that measures inequality in income or wealth. The USA has one of the highest in the first world, the UK the lowest. In simple terms, this means that you have many people on the verge of starvation in the same country as a glut of billionaires and multi-millionaires. Do ultra-rich people exist in Britain? Of course, however they are far less numerous and thus only few hold the extreme political power that such a class is known for. This also means that the poorest in society (disabled, elderly, extremely disadvantaged, etc.) won't usually go hungry or without a roof over their head because of state-funded services.
Second, the investor' mentality that varies between the two nations. In the UK, despite gambling being legal and widely popular, Brits are wise enough to differentiate between gambling and investing. However, since the 1990s, Americans tend to view the stock market as a form of casino and they are willing to throw a lot of money away without proper research. In the latter case, this mentality causes both a lot of millionaires to be born overnight (at least if they sell holdings asap while the price is sky high) and a lot of millionaires to lose everything in the same exact period.
The fundamental difference between America and Britain is materialism. In America, being a millionaire is usually living on a different planet than the less fortunate. One can be a millionaire in America and send their children to private schools, fly a helicopter over the decay of impoverished neighborhoods, or anything else within reason. While theoretically one may do the exact same in Britain, the mentality in Britain prevents this.