If you have applied through one of numerous visa application centres outside the UK, you will get the decision within 3 weeks. If you have applied from within the UK, you will get your decision within 8 weeks. If you want to get a faster decision, you can choose a priority service when you apply. There will be additional cost for the service.
Add to the time mentioned above 3-4 weeks to prepare the necessary documents which you have to submit together with the UK Start-up visa application. A standard list of evidence that you must provide includes the following:
a valid passport or other document that shows your identity and nationality;
bank statements showing that you have enough money in savings to support yourself upon your arrival;
proof that you speak fluent English at least to Level B2 of the European classification;
tuberculosis test results (not for all countries);
an endorsement letter for your business idea from a government approved body. It confirms that you or your qualified legal experts have done great preparatory work and have skilfully presented your business idea to a representative of the approved body.
Obviously, all the evidence mentioned above must be translated into English. Provided that you approached reputable qualified immigration experts, any unexpected waste of time will be minimised, and you will obtain the UK Start-up visa in the shortest time possible.