Compared with North America, you don't need to have any local trading licenses or registrations. There are no requirements for lawyers to draw up articles of association and register (accountants just use pre-approved templates).
Opening bank accounts was simpler (and much cheaper in my experience) too. You just take in your ID and confirmation of the company registration. Most banks will give a deal and many even have free banking. North American banks are generally eye-watering in their fee scales in comparison.
Having done both, the UK is way simpler, quicker and less onerous than North America. It also opens up the entire EU as you don't need to keep registering or licensing in each place (unlike in North America).
On residence/citizenship (note, NOT required to have a UK company!), the UK is a pain in the ass. They have become all crazy about immigration and put all sorts of obstacles in your way.
Find a different EU country for residence - forum shop. Some grant based on even a small amount of heritage (like multiple generations back) and some grant based on ca$h. If you have a few hundred thousand $, you should be able to buy your way in. Otherwise, a business startup with employment within a number of months is another route.
Once you have EU citizenship in one country, you have a Charter Right to go to any other you please.