Is this really an improvement in sex offender law?

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It seems to me there's still a lot of wiggle room for sex offenders who don't bother to register or to notify police of anything.

https://www.gov.uk/government/publications/crime-and-policing-bill-2025-factsheets/crime-and-policing-bill-management-of-offenders-factsheet

We are going to strengthen the notification requirements for sex offenders, give the police a power to prohibit sex offenders from changing their names on official documents and issue statutory guidance for the police to follow when disclosing information about sex offenders to prevent sexual harm.

Looks good to me.

Enable the police to serve a notice to offenders requiring them to seek the police’s approval before changing their name on specified documents (UK passports, driving licences and/or immigration documents).

That's good - but there's a notable omission in that list.