Can't help but feel we are incredibly lucky to have a free press in the UK. A free (and very aggressive) press means that snooped-upon data about MPs themselves will become valuable enough, and considered public interest enough, that it'll get purchased and published, which in turn motivates MPs to vote against its collection in the first place.
I agree that many politicians wouldn't care about privacy unless they themselves were threatened, but I also think David Davis and Tom Watson genuinely care about everyone's right to privacy as an ethical matter.
Depends on which bits of the press and how free you think it is. The large rightwing sections are quite happy to argue for more government surveillance against the usual suspects, and the press is still very much subject to the Official Secrets Act, D-Notices, libel considerations, etc.
I would much prefer that the press focussed on bills being proposed and those in the initial stages of the process, rather than pretend to be apoplectic when terrible legislation gets royal assent (i.e. too late).
We absolutely need to be more worried and indignant over legislation in the very initial stages, regardless of the risk of 'crying wolf'.
One of the problems with the DRIP bill was that because normal parliamentary process was not followed the press and public did not have time to get into the meat of the bill prior to it being passed. With for example the snoopers charter (version 1.0) there was time for the implications to be discussed in public.