Culloden Goes the Other Way...

[Insula Dei]

...or whatever is needed for a Stuart restoration. (Probably a Jacobite offensive in the South earlier that year?)

Is this at all feasible? What would Britain have looked like by the turn of the century?

(Very broad question, I know)

[politicus]

Bonnie Prince Charles only way to victory was if he and his 5000 men had rushed to London in 1745, before the duke of Cumberlands 10.500 man strong force could catch him, trying to provoke a popular uprising instead of turning around in Derby. Once he left England the rebellion was doomed. The government had strong forces in southern Scotland and Cumberlandsarmy in England, but some historians believe he could have made before being cut off.
The Hannoveranians were unpopular among Londoners, especially the lower classes, and they might have rebelled to support him if he had continued south. In fact the London Tories had promised to do so. But it was a gamble, and he chose not to take it.

If he had won, he would soon have encountered the same difficulties as earlier Stuarts. Absolutism in the continental style was never going to work in Britain. So perhaps a coup by Whigs a decade later?

The Scottish highland culture might have been preserved to a greater degree, since it wouldnt have been explicitly forbidden.

[Tetro Kornbluth]

Not realistic really (unless you change the European geopolitics of that exact moment and the competence of 18th Century French naval officers enough for it coincide with a French invasion of the island). But for the most likely 'Stuarts maintain control of England' timeline probably the best option is the failure of William of Orange's invasion in 1688. This though would probably have a required a French invasion to succeed in the long run but England would not have been prepared at all for that in the late seventeenth century.

As for how different it would be, I'm too tired to speculate right now but I do know that the history of Ireland would be unimaginably different from what transpired in RL without the post-1688 constitutional settlement and then James II's hash handed attempt to regain the throne by invading Ireland. Another thing to note would be problems for England's mostly still tenuous colonies on the other side of Atlantic...