Diminished Responsibility is a partial defence to a murder charge. It must be proved by the defence to the satisfaction of the jury on the balance of probabilities.
The CPS website covers this in detail - there needs to be an abnormality of mental functioning that
"Abnormality of mental functioning means a state of mind so different from that of ordinary human beings that the reasonable person would term it abnormal. It covers the ability to exercise willpower or to control physical acts in accordance with rational judgement. It is a question for a jury. They are not bound to accept medical evidence: R v Sanders [1991] Crim LR 781. "
And that
"Impairment must be substantial, there must be evidence of this and it must be raised by defence, c.f. R v Campbell [1987] 84 Cr App R 255, R v Kooken [1982] 74 Cr App R 30. The new section 2(1)(b) states that the abnormality of mental functioning must have substantially impaired the defendant's ability to do one or more of those things as mentioned in the new section 2(1A):
a) to understand the nature of the defendant's conduct;
b) to form a rational judgement;
c) to exercise self-control.
Subsection (1B) provides that an abnormality of mental functioning provides an explanation for the defendant's acts or omissions in doing or being party to the killing, if it was at least a significant contributory factor in causing the defendant to act as he did. This does not require that it should have been the only cause or even the most important factor in causing the behaviour. But it must be more than a merely trivial factor. The defence should not be able to succeed where the defendant's mental condition made no difference to their behaviour - when they would have killed regardless of their medical condition.
It is for the defence to prove that the person is, by virtue of this section, not liable to be convicted of murder. The evidential burden is on the defence on the balance of probabilities i.e. the civil standard (in contrast to Loss of Control, see below).
If diminished responsibility is not raised at trial, it is unlikely that the Court of Appeal will allow evidence that was available then to be called at appeal. It will not therefore substitute manslaughter for murder.
www.cps.gov.uk/legal/h_to_k/homicide_murder_and_manslaughter/#diminished
This is a high hurdle to meet so I am prepared to assume that the jury who actually heard the evidence was best placed to determine what she was guilty of.
I am fine with the sentence.