It would be odd to see the Information Commissioner (the UK's data protection regulator) as toothless, given it has so far been among the most severe in penalising large businesses under the much greater powers it acquired under the GDPR.
This could be more of a strategic move from Facebook, anticipating the UK government wanting a quick post-Brexit trade deal with the US and having limited practical room to manoeuvre in negotiating one. In particular, the UK government presumably doesn't want to commit political suicide, so it's very unlikely to compromise on issues like the NHS or food standards. That means it needs something else, and probably something big, that it can bring to the table. And that could well be favours for US tech firms that are already here, such as agreeing not to go after them for extra taxes and brushing anything resembling privacy protections under the carpet.
Whether that is a good bet for Facebook to make is a different question. If the Johnson administration doesn't manage to seal a deal very quickly -- and it does have a few other things on its plate right now, not to mention a known-hostile incoming Biden administration across the pond -- then there is a decent chance that any future US-UK trade deal will actually be concluded a few years later. By that time, our respective governments might well be led by Kamala Harris and Keir Starmer, for example, in which case Big Tech might have much bigger worries anyway.
But since no-one has a crystal ball, presumably those tech firms are going to try to insulate themselves from unnecessary risk in the fallout from Brexit, and this move by Facebook probably achieves that at a reasonable cost right now, regardless of what might happen some years later.