My parish is Oratorian, and the Blessed Cardinal is a great patron of mine; what a terrific WI!
I believe that Cardinal Newman (let us call him Pope Hadrian VII, after the only other English Pope, though he may well have chosen to be the first Pope Augustine, after his own patron saint, or Pope Philip, after the founder of his religious congregation) would have made a terrific Pontiff. He was of course an unswerving traditionalist in terms of doctrine, but he was a gentleman at heart, capable of engaging with both Protestants and liberal Catholics. He would have added a wonderfully intellectual and theological dimension to the Papacy, in a century which was filled with Popes largely concerned with
Let us say that some of the concerns Pius IX had with his theology are ironed out, and he is duly ordained a Cardinal in the early 1870s. I expect that he would have remained a Prisoner in the Vatican, like his predecessor. He was a man who always demurred to the authority of the Papacy, and I have no doubt that he would have maintained that the occupation of Rome by the Savoyards was illegal. Unlike Leo XIII, I strongly doubt that Pope Hadrian would have given tacit recognition to the French Republic; he was a royalist throughout his life. As for liberalism in the Church itself, I have no doubt that he would have attacked it as fiercely as Pope Pius X did; this is the man who wrote "For thirty, forty, fifty years I have resisted to the best of my powers the spirit of liberalism in religion, which is an error overspreading, as a snare, the whole earth".
I'm sure England would be very divided as to the new Pope; on the one hand, the greatest Empire on earth now can boast that one of their race is the spiritual leader of half the world. On the other hand.... he is a Catholic. Perhaps Pope Adrian might lead a stronger drive within the Church to bring the Tractarians back to Rome, though I doubt any major schism would occur. One major act undertaken in the reign of Pope Leo was the declaration that Anglican orders are invalid; I personally think that Newman would have made a similar statement.
I am sure that there would be more conversions amongst the English, and that the profile of the Oratory would be raised. In terms of Ireland, the new Pope had lived there for a time, and was warmly affectionate to the Irish. However, he never supported Irish independence; I could see a Papal encyclical disavowing the use of violence to rebel against the Crown. Pope Leo XIII canonised the English martyrs in the 1880s; I have no doubt that Newman would do the same.