Just like the Birmingham Six, the Guildford Four, and the Maguire Seven were all convicted apparently absolutely safely on apparently watertight forensic evidence, confessions and circumstantial evidence relating to their association with IRA members. The 'rot in jail/throw away the key' rhetoric was just the same.
The Birmingham Six were convicted in 1974, their first application for leave to appeal was refused in 1976, and again in 1988 (after a series of documentaries questioned the evidence and produced new evidence) their convictions were ruled safe and satisfactory. Until 1991 when their second full application for an appeal was allowed by the CPS, and they were freed after 17 years in prison. It took another decade for them to be offered compensation.
It was this and other related miscarriages of justice that caused the CCRC to be set up in 1997, because of diminished public confidence in the effectiveness of British justice.
Which is not, of course, to say that Lucy Letby is innocent.
Only that high-profile miscarriages of justice have in fact occurred in the relatively recent past (Sally Clark's conviction for the murder of her sons was quashed when the CCRC referred back to the Court of Appeal), and the safety of those convictions was upheld by the judiciary throughout the appeals process, for decades in some cases. The fact that a jury heard evidence and came to a verdict in two separate trials in LL's case, and that a judge twice refused leave to appeal, is not necessarily convincing proof of guilt.