There is no such evidence of illegal immigration, only absence of evidence of legal status.

Of course there is. it may be harder to assemble than a presumption of illegality, but it is necessary in any system aspiring to be committed to justice. That's why courts have to prove guilt rather than the accused to prove innocence.

Evidence about the circumstances of how someone came here and where they came from can provide evidence of illegality. It would then be up to the individual to counter that, if it could be countered. In the case of the Windrush generation any proof of the circumstances of their arrival would in itself serve to undermine any accusation of illegal status. If the authorities wished to counter that they would need to find some other evidence that for some reason their presence was actually illegal.

As I asked, Keith, how would you go about proving your legal right to be here if challenged?