This basically pans down to the Greens or the Lib Dems. The former have just one voice, Caroline[0], in the House of Commons. The latter is led by the guy standing alongside the Prime Minister as this "emergency legislation" was announced, and offered his vocal support. In any case, the Lib Dems will also likely be ground in to dust in the coming general election: currently polling at <10%[1], down from about 25-30% prior to the last[2]. So, even if they were successful at moderating Government policy with respect to social liberties, they soon won't matter.
Won't help that much. The existing laws were actually EU laws that a previous UK government had pushed for, essentially using the EU's lack of democratic accountability to make sure voters didn't have a say in it. This happens quite a bit. The only reason they're resorting to this trick is because their usual EU-based one failed.
This would not have happened if the UK had listened to the ECHR or the ECJ.