Okay, a big mistake has been made, and it will all be sorted out. People who have suffered badly should (and I think will be compensated. Today, the news is that there are records of passengers on the Windrush in the British Archives, and that these can be used to help in this fiasco.
I, too, don't understand why School records, National Insurance records, tax records, etc. don't demonstrate that these people have been living and working here for years.
And in 2010, when the landing cards were destroyed, why weren't they data-based first?
The Home Office should be seeking out illegal immigrants, and deporting them, not hassling and distressing people who have every right to remain here as British citizens.
However, apologies have been made. And I am sure that - eventually - all this will be put right.