Facebook, Twitter, et al just need to announce that if this is passed into law, then sadly their services will no longer be available in the UK, as they wish to keep users in other countries secure. Once the public discover that the sites they are addicted to on the web will be taken away from them there would be an almighty uproar.
Just start bombarding your users with an information campaign. Fexit means Fexit. Twexit means Twexit.
At least this new lot are so stupid that they seem to be using their old boss's paymaster the Daily Telegraph as their Pravda. Behind that paywall, few will be exposed to all the propoganda.