ie what matters - both in interpreting todays laws and if they are insufficiently clear, drafting future amendments - is why the law was created in the first place.
The UK law is well drafted and makes it very clear that the aim of copyright is not to stop you copying something per se - but to copying something for commercial gain that is simultaneously damages the copyright owner. I suspect those principals are the same the world over - whatever the exact drafting.
So the question you have to address is do the actions of the AI companies fit these critieria.
Are they copying copyright material without permission - tick.
Are they making money as a result ( it's a commercial operation ) - tick.
Are they damaging the original copyright holders in the process - this is the only one remotely in doubt - but I'd argue it's pretty clearly a tick in many areas - bit bit less clear in others.
In terms of lobbying - it's the big tech companies that are currently trying to get the law changed in the UK - to make what they have done legal ( while stil arguing they haven't done anything wrong..... as laws are not typically changed retrospectively ).