The last time I was at the Tower of London, I followed the traditional advice to arrive right before opening. I stood in line with 100 other people following the same traditional advice. One of the workers told me, “If you just come 15 minutes after opening there is no line and you will walk right in.”
Today, I decided to follow his advice. We arrived at 9:15 (fifteen minutes after opening) and we walked right in.
For London Pass Users I can confirm there is no need to get any ticket in addition to your pass. They scan and in you go.