It would probably be Henry the 2nd, who had frequent conflicts with a Bishop going by the name of Beckett over precisely how independent the crown was from the Church's yoke. Some of his knights, overhearing him shout in frustration, "Will no one rid me of this accursed bishop!? (or something along those lines)" His knights took this for an order and went out to kill Beckett. In this time line, they accidentally alert those loyal to Beckett. Beckett deals with them, and for all he knows, they really did get that order. Henry is in the end tried for crimes against the Church and hanged. In our time line the seperation of church and crown that developed in England laid the ground for our separation of Church and State. By cutting this off then, it gives the Catholic Church far more power in England, as it had in France and Spain. As for how an Information Revolution could develop in such a theocratic state, I have this to say: A religious cold war between them and another country, such as Japan would result in the Catholic-controlled countries constantly having to develop their technology to compete. The American Revolution would be easier quashed if all of Europe is united against it, so that is the next question. What role does America play?
Beckett was archbishop of Canterbury..... and rose through the ranks of the church from clerk. How does he hold off three knights trained for war?
And even if he does, how is Henry II tried for the crime - in whose courts? It can't be the church, as their courts can't pronounce death sentances (which was what the spat between Henry and Thomas was about). The anointed, crowned Angevain would not allow himself to be tried in this way - he allowed his lands to suffer under an interdict until he carried out penance for the death - ITTL, there would be no greater punishment than in OTL.
And if he is killed, his shy, retiring peaceful heir would surely take it like a lamb... wait a minute - that's Richard I - unlikely to be the calmest of people, and such a execution almost certainly wrecks his Crusade.
I'm not sure that the death of Beckett really began the seperation of Church and State in England - mainly as it doesn't exist, they remain bound in the person of the monarch today. I think Henry VIII remaining with the Roman Church, and a proactive crushing of the Reformation - probably with a much earlier Counter Reformation - is more likely to produce a cyber papacy