A few months ago I came up with a hypothesis that in the U.S. the preference for nicknames or short names as full names vs. longer names as the given name varies across the saeculum, with the former increasing during 4Ts and peaking during 1Ts, with the latter increasing during 2Ts and peaking during 3Ts. I found more evidence supporting this; if you look back to the earliest years covered by the SSA list you'll see that nicknames as official names as well as "shorter" official names were fairly big during the 1880s and 1890s, fell off during the 1900s and remained low during the 1910s and 1920s, went back up during the 1930s and remained up until the late 1970s, went back down again around 1980 or so and has stayed down until very recently. If you compare the SSA list of 2010 to that of 2007 (before the start of the Great Recession) you'll see that although the nicknamey and shorter names are still far less popular than they are in the U.K. they are overall on the rise (the four names I used for the comparison are Ellie, Finn, Lucy, and Max; all four increased during that time). To be fair, Finn does have a strong pop-culture influence right now (Glee); even so Finn is on its way up in comparison to some of its "longer" forms such as Finnegan (which remained nearly steady between 2009 and 2010). My prediction: Although I don't think the more extreme "nicknames as full names" that are currently popular in the U.K. (such as Alfie or Millie) will catch on in the U.S. I think the phobia of nicknames or short names as official names is on the wane with more "just Finns" or "just Lucys" rather than superflously going for a longer form on the birth certificate for the sake of formality.
Now for the question that many name enthusiasts have been wondering: Why has the U.K. loved the nickname trend in recent years while the U.S. has not, when it's the U.S. that is traditionally less formal in its lifestyle? Well, the Strauss and Howe saeculum may provide some insight here as well. During First Turning (High) eras (such as the 1950s or 1870s) community bonding is up while individualism is down; during Third Turning (Unraveling) eras (such as the 1990s-2000s or 1910s-1920s) community bonding is down while individualism is up. At the present point in history (though it's not always been the case) the U.S. and U.K. are closely aligned in their saeculae (in other words approximately in the same Turning era). During High eras, desire to bond in with the prevailing culture persists; at these times we have less formal names ruling in the U.S. and more formal names ruling in the U.K. During Unraveling eras, desire to have a name that marks one as an individual persists. In the U.K. this means scaling down from the formal prevailing culture and using informal names, while in the U.S. this means scaling up from the prevailing informal culture and using more formal names (notice how during this era Americans were obsessed with "becoming and looking rich" with McMansions, SUVs, etc., and likewise tended to use baby names that present such an image; in addition this was one of the few times in recent history that American schools were seriously considering school uniforms [which are common in the U.K. all along] but the talk has since largely subsided). I do not have any official statistics on U.K. names available other than those from recent years, but from what others have said I've been able to extrapolate that Britain follows a cycle on name formailty that is about equal in length (~80 years or so) but runs opposite to that of America's.
Once again, remember that this post is a generalization of trends.