So, apparently the thing that's called "leaving in the British way" in Russian and French (not surprising, Russian has lots of French expressions) is known as "taking French leave" in the UK and "Irish goodbye" in the US and UK.
https://qz.com/quartzy/1163220/tis-the-season-for-the-irish-goodbye-the-french-exit-or-to-leave-the-english-way/