Not overnight, but over several years, quite possibly given the right conditions. It's important there are strong safeguards against this happening.
Just a few years ago there was a case of British police working with companies to spy on those engaged in trade union activities and help to destroy their careers. With unfettered access this kind of activity could become commonplace.
The security services can already access e.g. Facebook messages and email with a court order and approval from a judge. They cannot access end-to-end encrypted messages. What you are proposing is preventing internet companies from offering end-to-end encryption. This is not exotic technology. The mathematics required has been available for decades. Anyone can download the code needed to rig up an unbreakable end-to-end messaging system. Stop people from communicating via WhatsApp securely and normal people and companies will have their communications exposed to theft and the baddies will move on to other easily obtainable methods of communicating securely.
(By the way, the Paris attackers communicated via SMS, which is not encrypted, and so the regulations you propose would have made no difference there.)
http://www.itv.com/news/2017-03-26/...rror-strategy-flaws-after-westminster-attack/
The police have never actually operated on a shoot to kill policy. The aim is not to kill the terrorist, but to prevent the terrorist from causing further harm. The death is just a byproduct.