Working Remotely for a US company while living in UK

I was recently laid off, and it'll be a few months before we can begin the spousal visa process due to some health things that require tests and possibly surgery before I move. If I need surgery I would much rather have it done with doctors I know and trust than while navigating a brand new health system! 

So onto my question - I have to job hunt to collect unemployment, and in my field there are quite a few fully remote opportunities. Is it difficult to continue working for a US company while living in the UK? Does it create a lot of tax issues? Some of them also have UK divisions so it's possible I could transfer, but usually companies want you working for them for at least a year before doing that. I'm already going batty with no work, I've signed up for 3 coursera classes in my field to help occupy my time and learn more but I would rather have a source of income too!

Not sure about US/UK but I have a friend who lives in Madrid and works for a company in Edinburgh - taxation took a couple of months to sort but runs smoothly now.

It's easiest to be a set-employed contractor.  Otherwise your company would have to issue you a UK work contract meeting all the legal requirements of the U.K.  You'll bill the company and then pay tax to HMRC.  Then when you file your US return, you'll either take the exemption or tax credits to avoid double taxation.

You would need to work for a US company for a minimum of one year (might even be longer now) for them to sponsor a Tier 2 ICT visa.

We are married now so it'll be a spousal visa when I move not tier 2. When I mentioned transferring it would be as a local job with the same company, most just want you to work for them for a minimum of a year before they'd consider letting you change jobs/positions within the company - that's a policy I've seen for many employers here. I just don't think any company would hire a person that's moving soon unless I could provide some sort of assurance that I could keep working remotely from the UK. Being a contractor could definitely be an option, if I manage to get an offer I'll see if they could do that. Thanks