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The law as it is now is that if you don't register for SS/pre-SS, you WILL lose the right to live/work/healthcare, or to put it in newspaper terms, become an Illegal Immigrant.

So, you will be fine. But people in care homes with dementia or people in homeless or other shelters with no paperwork that cannot apply or people that don't know won't be.

The HO knows that it is impossible to get everyone to register in time. That is not a fault of the UK, Spain/USA never managed it either. Registration after people arrive is just never going to work well. With the SS app they are doing what they can, though that process is also quite buggy and people often get the wrong status.

But instead of making provisions and getting people to register as they do, but let everybody that miss the deadline register when they are found, they just declare all those people illegal immigrants.