You don’t get it.
The size of the U.S. and British economies before the stock market crash is not the issue. What happened to these economies after the market crash is what matters in this discussion.
Unemployment may have been higher in Britain before the crash than it had been in the U.S. before the crash (I don’t know since I don’t have stats for Britain), but unemployment in the U.S. after the crash was far more severe than it was in Britain after the Crash.
Economic output may have been higher in the U.S. before the crash than it had been in Britain before the crash (again I don’t have any stats for Britain), but economic output in the U.S. declined more than it did in Britain (in terms of the time needed to recover to pre-crash levels).
Per capita income may have been higher in the U.S. before the crash than it had been in Britain before the crash, but per capita income fell more in the U.S. than it did Britain after the Crash.
There was essentially no Great Depression in Britain and the British social welfare programs likely deserve the credit.
Britain may have been in recession before the stock market crash (this is likely wrong; Britain may have had a smaller economy relative to the U.S. but did that economy actually meet the textbook definition of recession?) but much of America was also suffering recession before the crash. American farmers were deep in debt and suffered from market prices that were often lower than the cost of production. And American farmers enjoyed little of the alleged economic prosperity of the Roaring Twenties (much of the boom of the 1920s was fueled by electrical appliances but by the 1930s only 10% of American households had electricity).
But because America did not have Britain’s social welfare system the stock market crash allowed that recession to become the Great Depression in the U.S. The market crash did not do as much damage to the British economy as it did to the American economy because Britain had a social welfare system that keep the recession from being as deep or as long as it was in the U.S. Get over it.
