Personally, if the couple is dead serious about each other, I would recommend that when it's possible, the UK resident goes to the US and they marry. As soon as they get their marriage certificate, they apply for a spousal visa. That way, they only pay for one 30 month visa (the process for "Indefinite Leave to Remain" is 5 years), when they're approved, they live together and don't have to worry about things for another 30 months and they can work, as soon as they get their NI number and they have the ability to access the NHS if they need to.
Moving to the UK is not for the faint-hearted or those who are cash strapped. It's a hell of an investment but hopefully, it's worth it. They could also apply to marry and move to the US, it's faster and cheaper.
The US fiance visa (K-1) process is not always quick and easy.
Some conditions:
You and your fiancé(e) met each other in person at least once within the 2-year period before you file your petition. You may request a waiver of this in-person meeting requirement if you can show that meeting in person would:
<span class="italic">Violate strict and long-established customs of your fiancé(e)’s foreign culture or social practice; or</span>
<span class="italic">Result in extreme hardship to you, the U.S. citizen petitioner.</span>
Covid would probably count as a reason not to have been in each other's company.
While this looks straightforward, a relatively brief relationship which has been almost entirely long distance may be queried. A USCIS officer might decide the British party just wanted a green card. Telling them that the ultimate aim is to leave the US and go to live the UK might raise an eyebrow too.
It is doable, but the parties will ultimately have to do separate interviews in which they will be asked all sorts of details about the relationship, and getting facts straight and convincing the officers that the relationship is the real deal will be important.
Ask on the US expat board mentioned upthread if anyone has gone through that process.