The mens rea of murder is intention to kill or cause grievous bodily harm: R v Vickers  2 QB 664.
What is a Human Being?
A ‘human being’ is traditionally defined as a ‘reasonable person in rerum natura’. This definition encompasses any human born alive and has not yet died: Attorney General’s Reference (No 3 of 1994)  AC 245. An unborn child is not considered a human being for the purpose of criminal law, and so cannot be murdered.
However, if a child is injured by an act in utero and is subsequently born alive, but later dies, they are retroactively considered a human being for the purposes of murder and other homicide offences: Attorney General’s Reference (No 3 of 1994)  AC 245; R v Senior (1832) 1 Mood CC 346. The baby does not need to have breathed and the umbilical cord does not need to be cut: R v Reeves (1839) 9 C&P 25. This is a unique exception to the rule that the actus reus and mens rea must coincide and does not apply to non-homicide offences: Criminal Injuries Compensation Authority v First-tier Tribunal  EWCA Civ 1554.
When does a Person ‘Die’?
A person is considered ‘dead’ for the purposes of the criminal law if they have suffered brain stem death, even if other bodily functions continue (for example on life-support machines): R v Malcherek and Steel  2 All ER 422.
The usual rules for causation apply, with the caveat that accelerating death also counts as causing death: R v Dyson  2 KB 454. For example, causing someone with a terminal illness to die earlier than they would do otherwise is causing death.
Exceptions to the Actus Reus of Murder
The Queen’s Peace
The reference to the ‘Queen’s peace’ in the traditional formulation of the actus reus of murder is designed to exclude killing foreign enemy combatants in times of war: R v Page  1 QB 170.
A medical practitioner does not commit murder if they administer pain-relieving drugs with the purpose of alleviating suffering: R v Dr Bodkins Adams  Crim LR 365. This is an exception to the principle of oblique intent. This does not apply if the primary purpose is to euthanize, however: R v Cox  12 BMLR 38.
Grievous Bodily Harm
Grievous bodily harm is defined as ‘very serious harm’ and given its ordinary meaning: R v Metheran  3 All ER 200. It can include recognised psychiatric illnesses: R v Ireland  3 WLR 534. Whether the harm is sufficiently serious is a question of fact for the jury to decide.