Should the UK now allow the security services to access everything that we do online, in the light of recent terror plots, or are our civil liberties more important than the perceived benefits of more surveillance?
No, I don't think allowing any governmental agency that much power would be beneficial at all! To answer your question - our civil liberties are far more important than any 'benefits' that could arise from any more surveillance.
In fact, pretty much every terrorist that has carried out a major attack in the last decade has been known to western security services. The problem is not knowing the terrorists, it's acting on the evidence they have. More targeted surveillance could be an option, but more surveillance for all is absurd.
The recent murder in Woolwich is a good example. Both suspects were already known to the security services, and in fact MI5 had already 'approached' one of them.
I don't believe creating a police state is an effective way of reducing terrorism. Our civil liberties are far more important!