Linux - Forcing 24-hour locale?

Locales can be set for various components separately, so you can set LC_TIME to either "en_GB.UTF-8" (Great Britain), "en_DK.UTF-8" (Denmark – ISO 8601 time), or "C" (no locale).

(Don't forget /etc/locale.gen.)

As @grawity reports, you can try to find another locale for LC_TIME, but you will always have granularity problems, always compromising between options. This is a known problem and I suggest that you add yourself to the following bug report: Ubuntu Lauchpad bug #1392699