Partner has swiss job. I am uk citizen sole trader limited company, can I move?

It does not matter how the company is established here, it won’t entitle you to a permit. The company would still have to demonstrate that there is no one in the EU/EEA/CH available to take the job and it must coincide with the Eurostat labor market figures.

Of course it matters, the OP would still have to find a job with an employer who can satisfy the third country criteria... the payroll company is just a payment method.

In short, this is extremely challenging. It's essentially a hard-no. I am not sure about the US and green card, but imagine something similar. Brexit changed everything for situations like this; your only way in really is this concubine permit (unless you get married), and that only allows you to be here, not work.

How on earth can you write "It's not Brexit" and "Can you get an Irish passport?" in the same sentence, with a straight face?

Keep in mind also another thing...do you and your partner actually live together, and if yes, can you prove this?

From my experience dealing with the Zurich authorities, they'll want to show proof of joint residence for at least 1 year. And you also need to give a valid reason why you can't marry right now.

Don't have too much hope on this Concubine permit...

If you are not married, then the chances of being able to move to Switzerland with your partner at all are extremely limited - regardless of the work situation.

If you get married before she moves and takes up her job, then you can come over under family reunification. Technically it’s not guaranteed, but in practice it’s not a problem, certainly on a B permit. You would, however, need to register for a language course at A1 if you don’t already have the equivalent knowledge of the local language.
See Art 44 of the FNIA (link below)

If your then wife gets a B permit, then you will be able to work as employed or self-employed anywhere in Switzerland. See Art 46 of the FNIA (link below). In practice, that would mean that you could most likely be what’s known as “ANOBAG” while still employed by your UK company (assuming it’s a ltd or plc). “ANOBAG” means "employee without an employer paying Swiss social security, so effectively you would pay both employer’s and employee’s contributions here in CH.

If, however, your wife were given an L permit, there is no guarantee you would be allowed to work at all.

All this assumes your future wife is also non-EU. If she happens to have an EU passport, you would have no problems (but would still need to get married).

FNIA:
https://www.fedlex.admin.ch/eli/cc/2007/758/en

(when reading the law, “residence permit” means a B permit, “settlement permit” means a C permit (permanent residence), “short-stay permit” means an L permit).

That is a non starter since the OP is a one man company in addition to the OP not having a right to establish a business.

If the OP moves the center of management of the company moves with him so it is no longer considered a UK based company and that opens a a whole new minefield of issues relating VAT, social security and corporate taxation. On top of which the UK does not fully recognize the concept thus it could impact the issue of customer invoices etc....

Did you read Art 46 of FNIA?

So providing he is married, he can continue what he's doing on an s/e basis in CH, or be an employee of a non-Swiss legal entity as ANOBAG.

Of course, it all hinges on him marrying his partner before she moves to Switzerland so as to take advantage of family reunification and her getting a B, not an L.

Point of order:

No, you're not. You can either be a sole trader in the UK or operate through a ltd company. From your description, it's the latter.

Do you have any idea at all of the consequences of place of management of a foreign company being designated as Switzerland, because I do.