"rather importantly" is a correct and usable phrase in written English.
You can use it when you want to emphasize the importance of something. For example, "Rather importantly, the survey results showed a clear trend."
As for immigration, well, I note only this: Scottish attitudes towards immigration are much the same as those pertaining in England (though without, rather importantly, having experienced the same levels of immigration).
During the flight Octavia has set the manuscript on her tray table, where it is "displayed rather importantly, as if it were a prop in a play no one else realizes is being performed".
Finally, and rather importantly, someone will need to find the appropriate balance sheets before they can be taxed and many are located in tax havens.
The land--and what exists rather importantly underneath it--is seen by outside interests, and among many in this small town--as a commodity rather than anything mysterious or magisterial.
It will also, and rather more importantly, wreck more than four decades of British economic and foreign policy.
So does his place in history and, rather more importantly, his country's place in the world.
But fortunately for my peace of mind, and, rather more importantly, for the prospects of everyone on earth, it is almost certainly baloney.
Ideally Jennings will bring freshness and energy to the camp and, rather more importantly, much-needed runs at the top of the order.
How (or rather more importantly, why) did skateboarding transition from being a lifestyle to a sport?
Now that would be revolutionary -- or rather, more importantly, on a human scale -- evolutionary.
Finally, and rather less importantly, we had to decide whether or not to acknowledge the specific theoretical origin of each statement by assigning it the name of the component of NPT to which it referred.
