Charles I was totally different circumstances. He dissolved Parliament several times and tried to put parliamentary leaders in jail, because he wanted money to fight a war, which they wouldn't give him.
Its totally different now. You can't dissolve parliament and the King does not/cannot demand taxes of any type.
And so they fought a bloody Civil War, beheaded the King, then when Cromwell died, and his son didn't want to take his place, they brought Charles II, son of Charles I, back from exile, but when he died without a legitimate heir, they decided to give his brother James Stuart a shot at the throne, but then they deposed him, and forced him to flee the country because he was a Catholic, and they next went to Holland to beg William of Orange and his wife Mary, who was James Stuart's daughter to take the throne.
If you've read anything on Charles I, there was no way he was going to roll over for the January 6th committee that tried him, and condemned him to death. He firmly believed, as had British monarchs that had gone before him, that they had a divine right to rule, given to them by God. He died believing that.