Yes, you need to apply to the bank to open a business bank account, just like you need to apply for any other type of bank account. There is no guarantee that your application will be approved - it depends on the bank’s criteria and the results of your credit check - but most applications are processed within a few days.
To open a business bank account, you must be able to prove that you have a legitimate business. You will be asked to provide information about yourself and your business. If you will be operating as a limited company or LLP, you will have to provide your company registration number to confirm it’s legal existence. Some banks may also wish to see your incorporation documents.