Point of Divergence
In OTL, the opening of Parliament was postponed in 1605, so allowing the famous Plotters gunpowder to decay and become useless. The Parliament was postponed because plague made going to Parliament dangerous. However in TTL, a hotter summer kills off the remnants of plague and Parliament is opened in October as scheduled. The gunpowder is still lethally effective and some plotters haven't been given the chance to betray their fellow plotters. King James, Queen Anne, and both Houses of Parliament have gone sky-high together, leaving the Catholic conspirators ready to seize the kingdom.
The plan of the plotters was that while Guy was blowing up Parliament, most of the others would be making for the Midlands, to seize the dead king's elder daughter Elizabeth, from her residence in Warwickshire, and start an armed rebellion there which would spread out to take over the country. The king's elder son, Henry, died with his parents, and the younger one, Charles, was to be taken prisoner at London before the conspirators pulled out, and then brought up to the Midlands to join his sister. However all did not go to plan. Most English people were Protestants and the few Catholics were appalled by the act of violence.
They were in no physical or emotional position to support the rebels, and they were surrounded by Protestants who were hearing of the atrocity in the capital and the uprising, aware that Catholics were responsible for both, and left under the command of their surviving local leaders. The English took up arms in a panic, turning upon the Catholics in their respective areas, and imprisoning or slaughtering them, in an English equivalent to the wave of hate and fear that had, in France, driven the Catholics to massacre the Protestants there on St Batholomew's Day in 1572.
Protestant militia and vigilantes converged on the rebels in the Midlands and overwhelmed them. The conspirators fortunately had not murdered the royal children when surrounded. Their actual conduct when brought to bay was that of a high-minded resignation to martyrdom.
New British Order
The Catholic powers of Europe protested at the slaughter inflicted upon their co-religionists, but the murder of the king, queen and peerage would have done much to excuse it in the eyes of foreign states.
Charles I became king at the age of four. He never had the difficult relationship with his parents that left him determined to abandon most of his father's policies in OTL, and never have made a friendship with his father's unpopular favourite, Buckingham. In TTL he comes to the throne outstandingly popular.
He revered the memory of his murdered parents, and acquired an abiding hatred of Catholicism, and tended to the evangelical wing of Anglicanism. This made him much more popular in both England and Scotland.
His sister married a Protestant German prince, and when he lost his lands to Catholic powers, our, zealously Protestant and anti-Catholic, Charles would have entered the war wholeheartedly on their side. As a godly Protestant prince, with all the serious and devout nature of the real Charles, he would have been assured of considerable support in Britain.
The financial system was under serious strain already, and collapsed under the war effort, but the accord between Charles and his subjects provided a much better basis for an overhaul of it to strengthen the monarchy.
The Catholic majority in Ireland, faced with such a hostile king, were moved to rebellion, but the end to that was the crushing of the Irish Catholics by Cromwell much sooner, and under the control of a secure and popular king.
The Irish problem was solved by a programme of mass confiscation and mass evangelisation, leaving three Protestant kingdoms under one monarch. Thanks to the Catholic October Plotters, the British state was turned into a Protestant absolute monarchy as Sweden, Denmark, Saxony and Prussia all did in the course of the 17th century; but much stronger than any of those.
All the Kingdoms of the British Isles were now reforged. Presbyterianism from Scotland found its way south, bringing England and Scotland closer together religiously. Ireland had been crushed for now. 17th Century (October Plotters)