And what makes you think that this or similar laws will be abandoned by any UK gov after Brexit?

I don't think it will but I hope that it will. The rationale for such hope is that HMG is enacting Brexit and therefore logically* should be at least hesitant in rushing through any last-minute horror shows like this for fear of a public backlash. Also they are in the happy position of being able to play wait-and-see: they can simply see how bad this is for the rEU after implementation there (and it has the potential to be very bad indeed) and then decide at a later date to shelve it completely.

Do we know who benefits from this law? Who lobbied for it?

The audio and video rights holders will and did.

* Yes, I realise the humour potential in this.