The Queen does have at her disposal the Queen's Guards. She could order them to seize Johnson and sequester him in one of the basement rooms of Buckingham Palace. That might be more practical than sending him to the Tower, although, in the Tower, Johnson could be confined to the room used for Sir Thomas Moore, but that might interfere with the tourist trade unless he was made the main attraction. I believe the Yeoman Warders are still part of the royal household guard.

"It is not necessary to have hope in order to persevere."