I don’t think you’ll be able to do that...

@Derek Fulton How long are you planning on staying next/each time? All visitors need to demonstrate that they meet Immigration Rule V 4.2 (b) “will not live in the UK for extended periods through frequent or successive visits, or make the UK their main home.” The typical rule of thumb is to spend at least the same amount of time outside the UK as in it. Travellers who need to visit the UK regularly over a longer period can apply for a long-term Standard Visitor visa that lasts 2, 5 or 10 years, for a maximum of 6 months stay on each visit. But as a US citizen you can already do that

I hope OP is not using his real name. Even if UK immigration do not monitor this site actively, any detour via secondary inspection will nearly certainly have them come up with this question and all the big red flags it raises. If you want to live in the UK you’ll need to look into settlement visas, otherwise you’ll run into trouble.

Is a marriage certificate a possibility ?

"Even if UK immigration do not monitor this site actively," - they do.

And they can do this

@jcaron I don't really want to stay more than 6 out of 12 months. I just want to come and go intermittently without having to worry about it.

@DerekFulton Then space your visits out and go back to your home country in between them. Demonstrate that your UK visit pattern is that of a genuine visitor - someone who has compelling ties to their country of residence. And don’t overlook tax implications of spending a significant amount if time in the UK gov.uk/tax-foreign-income/residence

@jcaron - Why do you hope he’s not Using his real name? That’d only be an issue if he wanted to do something illegal, and you were actively encouraging him to do so! But as far as I can see, the OP has no intention of circumventing immigration rules.

@ChrisMelville OP has heavily implied that they are already breaking UK immigration rules. They say that they "work remotely" implying that they are working in the UK. This is not allowed for entry opn visitor visa/without a visa.

UK authorities absolutely do care, and have sent pplenty of other Americans home for working remotely in the UK - we have multiple examples of that on this very site.

@CMaster I couldn't find any—could you perhaps link one? Chris Melville is exactly right—I'm paid by a German company. No way I'm taking a Brit's job.

More broadly though, what you are decribing wanting is being a (part time) resident, not a visitor. You may not have aspiraitaions to move perementantly but for hte next ~3 years you desire to be a resident of bnoth the UK and US. Sadly, I'm not sure if the UK immigration system gives you a good way of applying for that.

"work remotely" is a big issue. What's to prevent you from working remotely while in the UK, Germany, US, or anywhere else? That explicitly eliminates a job-related tie to the US...

As a suggested "fix", have your girlfriend come visit you in the US. Maybe a 3-month cycle - you in the UK for a month, her in the US for a month, then a miserable month with each of you in your own country. You still need to deal with the "remote work" issue to ensure you're not running afoul of any laws and taxation issues.

That visa is called a Marriage Certificate! :)

@FreeMan Yeah I think I'll do that. Just work in the US, and whenever I come visit her in the UK, just take that time off work. A true visit of leisure—no work performed. But a bank balance to show I can support myself while I'm in the UK.

Just for the record, Chris Melville's input is to be taken seriously, as he is (was?) a UK border officer

@ChrisMelville Can you confirm that what OP describes is allowed visa-free?

There’s no official publication which goes into such detail. It’s the officer’s decision to make, and it’s a decision taken in the round. A clear breach of the rules is someone taking employment in the UK without permission. However if someone’s employed by a German company and just happens to log on to their laptop, it’s about the wider context. E.g someone on a short business trip is of course allowed to do this. So it’s not about using the laptop per se: it’s about whether, all things being considered, the person is effectively living in the UK (and also happens to work remotely).

To add to this - standard answer from a former immigration officer: You can’t be guaranteed of entry. If in doubt, you can apply for Entry Clearance. This means you can satisfy the authorities in advance, before you fly, to avoid extended questioning at the border. If you can satisfy the Entry Clearance Officer that you’re not intending to live in the UK, and have a reason to leave at the end of your visit, you’ll be fine. Just ALWAYS tell the full truth - because a lie won’t just lead to a refusal: it’ll lead to a ban.

Finding a closer girlfriend is also an option.