Few babies are abandoned in Britain these days, some years none at all, so there is no longer any provision for them. These babies were left, moderately well wrapped, where they would quickly be found and, individually, arouse little suspicion.
Elsa was abandoned at an hour old, so can hardly have been left by the mother.
They were born healthy and well nourished, no evidence of drugs or alcohol, and the mother was eating well in pregnancy. This is not a chaotic, inadequate, learning-disabled or destitute mother.
The most likely culprit is the father, with coercive control over a captive woman: possibly incest; a cult; possibly trafficked, modern slavery; but probably not prostituted (as all children have same father).
As well as the well-known Elisabeth Fritzl, there have been many such cases. There was one in Brixton ten years ago, where the situation had been going on for decades unbeknownst to neighbours:
https://www.bbc.co.uk/news/resources/idt-b0af7ef5-1031-4e1f-a3ac-b3c21ef0f932
The best hope of tracing the parents is through familial DNA, which the adoptive parents can have done even if the police have restrictions.
Meanwhile, although it is a high risk strategy, publicising the situation may produce someone nearby who suspects this household, and will encourage them to report it.
And it puts everyone all over the world on notice that Britain is not a soft touch – not a country that gives sanctuary to such coercive abuse. This discourages future occurrences of such tragedies – and prevention is always the best option in safeguarding.