The amendment referred to here by @tnewtondunn has been published. You can find it on today's amendment paper here. https://publications.parliament.uk/pa/bills/cbill/58-01/0177/amend/ukinternal_rm_cwh_0910.pdf

There follows a short thread explaining what this amendment does and what it does not do. https://twitter.com/tnewtondunn/status/1304103835674304512

The default rule about "commencement regulations" is that they are made by a Minister without any form of Parliamentary approval. By default, that is what would happen with clauses 42, 43 and 45 (the ones that break, and enable the Government further to break, international law).

This amendment would mean that the commencement regulations for each of those sections is subject to a further vote by the @HouseofCommons. A motion would have to specify which sections were coming into force and on what date.

This provides an additional "hurdle" before the regulations can made made that breach the Northern Ireland Protocol.

However, it doesn't stop the Internal Market Act, in and of itself, breaching Article 4 of the Withdrawal Agreement.

If MPs voted to allow the Government to bring these provisions into force, moreover, we would return to the position we were in before. For six months, the Government would be able to make regulations:
(a) without prior approval
(b) repeatedly
(c) which break international law

Only six months later would the Government start having to lay regulations in draft, and get the approval of both Houses, before they could come into force.

In practice it seems like the Government would try to commence these powers just before transition ends.

So for the first half of 2021, the Government would have a power to breach its international commitments, and Parliament would have no guaranteed ability to stop those regulations from being made. It would let the Government "set the agenda" for how these powers are to be used.

Given the statement yesterday by the European Commission, a compromise like this is unlikely to be accepted: it still involves a prima facie breach of the Withdrawal Agreement treaty, and requires the Government simply to win one Commons vote to start breaching the Protocol.

I should probably add, that this amendment's "lock" doesn't give any greater a role to the @UKHouseofLords in overseeing whether or not regulations can be made to breach international law. The commencement vote is confined to the @HouseofCommons.