Then there would still be the issue of influences of Rome that might slow down integration somehow. Maybe prevent that early invasion and ravishing of an early English King trying to get the Scottish Crown? Then the Lowlands might integrate into England naturally, followed by the Highlands. Wales gets Englishized a bit more as well, then the nobles and subjects of Greater England set up loads of plantations and integrate the area piecemeal.Wouldn't the best start be by having England and Scotland remain Catholic?
Then there would still be the issue of influences of Rome that might slow down integration somehow. Maybe prevent that early invasion and ravishing of an early English King trying to get the Scottish Crown? Then the Lowlands might integrate into England naturally, followed by the Highlands. Wales gets Englishized a bit more as well, then the nobles and subjects of Greater England set up loads of plantations and integrate the area piecemeal.
Well obviously this is OTL.
However the question of Ireland being absorbed in the same way as Scotland (an independent kingdom with the same king "voluntarily" joining a joint stock country) in the 17th/early 18thC is interesting. I think the only way is to make Ireland a protestant country.
My own personal try involved a massive Irish opposition to Henry 7 & 8 which tied Protestantism/calvanism to anti-English sentiment, the Pope did not make Henry the defender of the faith for nothing after all. A few years down the line Henry wants to get his leg over with Anne and Irish anti catholic feeling mutates slowly to Calvanist anti-Anglican feeling. By the time of Mary I it will be all protestants together against the counter reformation. That doesn't cure the problems of Ireland but it does mean the whole of the British Isles is united against the Evil Empire (TM) of Spain and then France.
Personally, I think the best way is simply not executing the Easter Uprising's leaders in 1916. That was the tipping point that made the Irish see themselves as not British.
The Irish already didn't see themselves as British at that point, although without the Easter Rising, they could have come to accept the idea of being part of the British state. You'd probably have a better chance at doing this by giving home rule in the late 19th century. Or, even better, continued and scaled up the initial phase of response to the potato famine.
Well, considering how as the Easter rising leaders were arrested and taken away, the Irish citizens were parading the Union Jack and booing the rebellion, I'd say they liked being somewhat British.
A handful of vocal protesters are not in any way a good representation of the views of the rest of the citizenry.