Sorry, but Google almost force you to use https these days. We (A&A) as an ISP, cannot log search history using https Google even if we wanted to, and no amount of money (and yes, the government will have to pay ISPs for this) will change that fact.
We also have no intention of logging web access either. It will be interesting to see what law you bring in. It will be interesting to see how much you think it will cost to pay every small ISP to install expensive kit to log this all (and retain it securely in accordance with DPA) and what happens when that ISP decides to sell its customer base to another new ISP over night, and eBay all that nice snooping kit you just paid for and delete all that data that was retained as old ISP no longer exists. Rinse repeat. "Andrews & Arnold Nov 2015 Ltd", "Andrews & Arnold Dec 2015 Ltd", anyone?
Or maybe we will make each and every customer an ISP themselves and we'll merely be "transit" for them, then they can each discuss the fee for imposing logging and secure retention of the search history for their home/office individually with the government. That would be fun.
Even if only the big ISPs are forced to do this - I hope that *lots* of their customers will DPA subject access request them on a regular basis for copies of all of the logs held.
I also hope that every time one of these logs associates web access with one person in a house when it is actually another person in the house, people will use their legal right to have that data corrected on those logs under the DPA, and report the incorrect data to the ICO.
Until all MPs have their full personal web and search history publicly available as a matter of course I cannot see anyone taking these ideas seriously.
Ironically, this week, having been in the US, I was using various wifi, and VPNing back to a FireBrick here. Almost all I do is https anyway, but VPN is an extra layer because "No idea what US or local wifi operators do with my meta data or whatever". I can see it soon being normal for the reverse - VPN from your home/office to "sane" countries so as to access the Internet without breach of your privacy.
Once we have exact details of the proposed law, I can provide a more detailed comment on this lunacy.