Sir John doesn't say that the concept of privacy itself is changing.
Blurring of public and private identities:
People are now more willing to place personal information into public domains, such as on the internet, and attitudes towards privacy are changing, especially among younger people. These changes are blurring the boundaries between social and work identities. The advent of widespread mobile technology and email enables more people to remain connected to their work out of hours. At the same time, posting mobile phone photographs and videos online has led to a cultural shift where many people broadcast their daily lives and experiences, ceding control over some aspects of identity to others with potentially serious consequences for later life. (p.2)
But other people do, see for example The changing definition of privacy, 'Like' it or not, privacy has changed in the Facebook age, Privacy in a changing society, Facebook's Mark Zuckerberg says privacy is no longer a 'social norm' and The concept of privacy is now impossible to sustain.
Which is odd because, think about it, when first balloons and then aeroplanes started to fly, no-one said that the concept of gravity had changed.
Beware salesmen telling you that the concept of privacy has changed and you're past your sell-by date if you don't know it, these days anything goes. They're wrong. The concept of privacy is staying right where it's always been and its strictures still apply.
What the Chief Scientific Adviser is saying is that the attitude to privacy is changing. He's wrong, too. As those who give up their privacy will find when the old-fashioned concept of regret overtakes them.