Sir is always followed by the forename or the full name, but not the surname.

With the correction to Dr. as others pointed out it should be Sir Brian, Sir Brian May, or Professor Sir Brian May. Additional the PhD suffix could be added.

Edit: he doesn’t currently have a professor position so that would likely be incorrect here. He was previously a university Chancellor so that may be more correct to use, though I am uncertain how the different terms would be used in this case.

> In the case of a military officer who is also a knight, the appropriate form of address puts the professional military rank first, then the correct manner of address for the individual, then his name

According to the wikipedia page. Professor has precendence over Sir, but Dr. does not and is thus overriden.