1. They're both British icons.
2. The the clock that faithfully triggers Big Ben's oh-so-recognisable chime (for "Big Ben" is actually the name of the bell, not the clock or the tower), has been ticking for 150 years today, and On the Origin of Species - the book that got its start in Darwin's notebooks aboard the Beagle - was published 150 years ago this year.
3. The man who built the clock, Edward Dent, also made a chronometer for HMS Beagle.
The Beagle had a whopping 22 chronometers, which enabled, as Fitzroy put it in his narrative of the 1831-1836 voyage, "a connected chain of meridian distances around the globe, the first that has ever been completed, or even attempted, by means of chronometers alone." This and other survey-related undertakings were the Beagle's chief purpose - not, as hindsight might tempt us to believe, to carry a young Charles Darwin around the world.
Bow of the sprit to @friendsofdarwin.