It is not noticeable to tourists, mind you. London, like any European city that wasn't actually flattened in the war, is rich in architectural assets that make it feel very posh--low rise buildings older than thirty or forty years are a luxury in most American cities. Walking around a European city, the diversity and beauty of the architecture is dazzling.
But the standard of living in any given profession is much lower. Preserving London's dazzling antique architecture has meant that most of the people I knew had much longer and more expensive commutes than their American counterparts would. They lived in smaller quarters that were hotter in summer and colder in winter. At any given professional level, you found British people doing things that only much poorer Americans would do, like bringing lunch, hanging their clothes to dry, or going without cable (though the Americans I knew said the cable wasn't worth it anyway). People in Britain are not poor. But they have a noticeably lower standard of living than Americans do. If they were doing it in 1960's vintage apartment buildings and tract homes, it would be quite obvious. When I lived there, I literally could not afford to eat meat regularly or take the tube to work, and as a consequence wore holes in my shoes. (In fairness, I was being paid in dollars and the exchange rate was awful--but I wasn't the only one walking to save money.)
I don't want to sound as if I'm saying Britain's a terrible place--it's lovely, and I miss it. But the amount that people are able to consume is much less than the amount Americans are able to consume, and many of the things they forego make real difference in things like personal comfort. (Based on my admittedly limited sample of British mattresses, they must be unimaginably hardy sleepers). Consumption isn't everything. But it is something, and that is what's being captured in the GDP differences.