I was part of the Los Angeles Ukulele Expo a few weeks ago, which also tried to break the record held by Japan, but we came up short, about 1050 people. It was fairly well organized, but I don't think they did enough to promote the event far enough in advance. Obviously England did an excellent job of getting the masses out. Seems the Brits are more "tuned in" to the uke, and being a smaller country makes it easier for so many people to come together.
Over 4000 is a daunting number to pull together, but I would think the US has more uke players overall than most any other country, especially with Hawaii. It would be great if in the next couple of years one of the bigger uke festivals would make a push to break the record. Using a stadium is a good idea too, would help to keep things organized, easy parking, preset sections for counting, etc.