The fact that Lord Browne is gay is not a matter of public interest and normally a newspaper would have no justification for revealing the fact. However, Lord Browne has been accused of lavishing BP shareholders' funds on his Canadian lover (allegations that he denies) and in order for this tale (which is clearly in the public interest) to be told, his sexuality had to be revealed.
There are often calls for a privacy law, which would prevent newspapers from publishing details about individuals' private lives but this case shows how problematic such a law could be and how the rich and powerful could use it to suppress investigation into questions of legitimate public interest.
UPDATE: I understand there is still an injunction preventing publication of the details of how Lord Browne met his lover, yet Robert Peston has revealed the details on his BBC blog, as has the Guardian. Brave, foolhardy or simply an oversight?
FURTHER UPDATE: Stephen Pollard is correct. Lord Browne should be prosecuted for perjury.