Cromwell took advantage of the chaotic situation in the country, launched a coup and started a military dictatorship. In fact, it is not much different from monarchy. Cromwell died, and the country fell into turmoil again, so people realized that it was not necessarily a good thing to have no king, and charles ii was restored.
When reactionary James II came to power and began to take bloody revenge, Parliament staged a palace coup to welcome Mary and William back and establish a constitutional monarchy. This move by Parliament is great wisdom, which not only ensures the stability of the political system and the country, but also draws lessons from the British Civil War and changes the monarch within its control. The monarch was welcomed by the parliament, which inevitably needed its support. Therefore, Britain made a smooth transition from absolute monarchy to constitutional monarchy and achieved a "glorious revolution" without bloodshed.
Secondly, overthrowing something must be bad and not conducive to the development of the situation. However, after the glorious revolution, the monarch and the royal family have become things that are integrated with British bourgeois politics. The monarch has not made any chaos or mistakes, but has played the role of national spiritual leader, national image symbol and British aristocratic temperament. Then, why not keep a royal family to maintain political stability and the country's lasting development?
Finally, it has something to do with the national characteristics of Britain. The British people have always tended to be conservative in history, and both political changes and economic policies tend to be prudent and do not want to take too radical actions. They tend to make steady progress, so maintaining a royal family with a long tradition has become something that the British are happy to accept. As long as there is no major obstacle to the development of the country, it will not abolish the royal family and cause turmoil.