It all depends under which category of tier 1 you are applying for and the type of business.
How will a business partnership impact my ability to participate in the tier 1 Visa program?
I will be partnering with a U.K. citizen in opening a small manufacturing facility in Birmingham. How will this impact my ability to participate in the tier 1 visa program?
You can be in a partnership when applying for an entrepreneur visa.
It shouldn't negatively impact your tier 1 entrepreneur visa at all. If you are joining an existing business, you will need payroll evidence to show the number of workers before you joined so you can show your net job creation in due course. But you say you are opening a business together so this won’t be an issue. In order to extend your stay, you will need to have registered as a director of the business within six months of having been granted the visa (or entry to the U.K., if you were granted entry clearance), have invested the 200,000 (if you had to show this amount in your application, as opposed to the 50,000 requirement) by the extension stage, and to have created two separate full-time roles for settled workers that would have existed for at least 12 months each by the extension stage. Going into business with a British citizen shouldn't compromise your ability to meet these requirements. The job creation would be attributed to you if you open the business together. To qualify for accelerated settlement after three years, you will need to show either job creation of 10 full-time jobs in that period of a 5-million turnover.
You can obtain a tier 1 entrepreneur visa having a British citizen business partner. You will be required to demonstrate that you have at least 200,000 pounds available for investments in a new or existing business in the U.K. In addition, you must be registered as a director of a company or be registered as self-employed.