Can independent researchers get a sponsored visa for the US or UK?

I’m an independent alignment researcher from Canada. I’m trying to figure out my long-term options (I want to move somewhere and stay there for several years). 

I have some special visas as a Canadian to go to either place, but I’d need to be working at a ”job” to be eligible for the visa. I could go to London on a 2-year visa without a regular job, but would need a job after that visa expires. It feels like a gamble going there for two years and then not having the ability to stay long-term.

Someone told me I should consider checking to see if I can work on this with a university. I'm not sure if they'd be up for signing off on my visa as long as I keep getting my independent funding?

So, what are the options for independent researchers who don't have US or UK citizenship? Are there any orgs that sponsor visas for independent researchers?

Note: I’m completely happy staying in Canada and mainly working remotely with collaborators (though I’d probably move to a Canadian city with a couple of other researchers), but I want to make an informed decision.