No-one can "fight" it without knowing what it proposes and what laws eventually emerge; and then must consider carefully what are its weaknesses and strengths. Blanket opposition based on knowing little about is wrong.
Besides, laws are made for us by our elected Parliament, so if you wish to oppose it, write a clear, reasoned and constructive letter explaining your concerns, to your MP.
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One, perhaps main, aim is to try to reduce the pornography too readily available to children, and to fight illegal material. The latter includes the paedophilic material that hogs the headlines, but most of the criminal activity on the Internet is financial, plus illicit trading of illegal goods.
There is also a vast amount of bullying via [anti]social-media sites that do nothing to stop it - perhaps as such action might compromise their own commercial interests .
It is not draconian. It is not to stop people using the Internet; but if it greatly reduces the risk of people being hurt by wrongful Internet use, then it is not before time and might even not go far enough.
So often we hear companies like Meta bleating about how many wrongful posts they have removed; while Elon Musk has made it harder for 'X' as he now calls it to do that, and Telegram refuses to use any moderation at all.
Occasionally these companies are fined very heavily for various offences, usually connected to their monopolism, but perhaps not heavily enough to make them think.
Not enough. I suggest the companies should do more than just remove offending posts. They should also permanently block the sender identified by URL (to obstruct new-name dodges), even the URL itself. While the directors of these companies should be personally responsible in law too, as they are in Corporate Manslaughter and other Health and Safety laws. It is their responsibility to ensure the moderators and technical staff have the resources, training and support to keep the site "clean" in law.
I do not fear the On-Line Safety Bill.
I do not use the Internet for anything unlawful or antisocial, be that viewing illegal contents or me bullying someone.
I do not use my computer for copyright-breaking "streaming", or as a TV without a TV licence (though these forms of theft are a separate matter).
I do not fear there might be any special controls or oversight of my use.
Why should I?