According to Stephen Horwath's book Henry Poole, Founders of Savile Row (Bene Factum Publishing, 2003), "Part of the point of the traditional Savile Row suit was that it was so smart, and so well made, that it was almost unnoticeable." He states further that World War I destroyed most of a generation of English males, leaving a relatively small pool of bachelors who were happy to dress unnoticeably because they did not need to compete for the attention of prospective partners.
After 1945 there were once again about as many men as women in the UK, which forced the men to be more noticeable if they wished to attract attention. This led to inroads in the English menswear market, first by the French and then the Italians - two countries where menswear exists in large part to support the pursuit of, shall we say, companionship - to the point that English suits are the exception among younger men in the UK today. Just as they are in the rest of the world.
Fortunately for the tailors of the Row, once partnered a certain strata of those same English males, and similar men from other nations, become less concerned with the opinions of those partners in a variety of personal matters. I am for example a customer of not one but three Savile Row-trained tailors. I am also smoking a Macanudo as I write this, and no thoughtful man is likely to adopt the cigar as a habit until he is firmly mated. Thus, I indirectly lend support to Horwath's notion.
Whether the story is true or not, the pursuit of attention in dress remains alien to most Englishmen outside of entertainment-related pursuits. The clothes lend themselves to established men in the professions rather than habitués of the smartest clubs. The eye registers that they look good, and fifteen minutes later has forgotten all about them.
Which is after all as it should be.