People visiting the UK on business require a Standard Visitor Visa.
This enables you to stay in the UK for up to 6 months.
If you are an academic on a research sabbatical this can be extended to 12 months.
You need to show that you will return to your country after your visit and you have sufficient funds to support yourself in the UK.
The earliest you can apply is 3 months before you travel and you will usually get a decision wishing 3 weeks of making the application.