England maintained the monarchy because:
1. Because it was convenient. After a defeated Charles 1st was beheaded, parliament became the power base but the military structure remained the same. England was a republic in all but name with Cromwell head of the table. When he died a vacuum quickly ensued - no one could agree on the way forward and England was facing turmoil. In stepped Charles 2nd - at the invitation of parliament - to provide stability. The monarchy though powerless retained its material privileges - to this very day - except that the Queen now pays taxes!!!!
2. We're jolly well nice people and don't like cutting heads off,( unlike the French who lopped hundreds of heads off in their revolution.)