Trust the Clockmakers' Museum to have rather precise opening hours. It's open Monday to Saturday from 9.30 to 4.45 on the dot.
The Clockmakers' Company is one of the City of London craft guilds and the oldest surviving horological institution in the world. Their museum boasts the oldest collection of clocks, watches and sundials in existence.
You can arrange a guided tour with the keeper, by emailing Sir George White at keeper@clockmakers.org. Don't be late though.