Lord Nicholls’ opinion in Re H (Minors)(Sexual Abuse: Standard of Proof)  AC 563 is generally held to be the leading authority on the burden of proof in sexual abuse cases. At 586C, he held:
“Where the matters in issue are facts the standard of proof required in non-criminal proceedings is... the balance of probability. ...
The balance of probability standard means that a court is satisfied an event occurred if the court considers that, on the evidence, the occurrence of the event was more likely than not. When assessing the probabilities the court will have in mind as a factor […] that the more serious the allegation the less likely it is that the event occurred and, hence, the stronger should be the evidence before the court concludes that the allegation is established on the balance of probability. ...
Although the result is much the same, this does not mean that where a serious allegation is in issue the standard of proof required is higher. It means only that the inherent probability or improbability of an event is itself a matter to be taken into account when weighing the probabilities and deciding whether, on balance, the event occurred. The more improbable the event, the stronger must be the evidence that it did occur before, on the balance of probability, its occurrence will be established.”
This position has lead to some confusion, with parties arguing that for allegations of sexual abuse, a standard akin to a ‘higher civil’ burden of proof was required. An attempt was made by Lord Hoffmann to clarify this issue in Secretary of State for the Home Department v Rehman  UKHL 47 at :
“some things are inherently more likely than others...[it] would need more cogent evidence to satisfy one that the creature seen walking in Regent’s Park was more likely than not to have been a lioness than to be satisfied to the same standard of probability that it was an Alsatian. On this basis, cogent evidence is generally required to satisfy a civil tribunal that a person has been fraudulent or behaved in some other reprehensible manner. But the question is always whether the tribunal thinks it more probable than not.”
The misunderstanding did not end there, and, in a manifest attempt to end the apparent confusion, Lord Hoffmann again in Re B (children) (sexual abuse: standard of proof)  UKHL 35 at , held:
“The degree of confusion which is possible on this issue is exemplified by the fact that despite the painstaking clarity with which Lord Nicholls explained that having regard to inherent probabilities did not mean that where a serious allegation is in issue the standard of proof required is higher....
There is only one rule of law, namely that the occurrence of the fact in issue must be proved to have been more probable than not. Common sense, not law, requires that in deciding this question, regard should be had, to whatever extent appropriate, to inherent probabilities. If a child alleges sexual abuse by a parent, it is common sense to start with the assumption that most parents do not abuse their children. But this assumption may be swiftly dispelled by other compelling evidence of the relationship between parent and child or parent and other children. It would be absurd to suggest that the tribunal must in all cases assume that serious conduct is unlikely to have occurred. In many cases, the other evidence will show that it was all too likely.”
It appears that the confusion as to the nature of the burden of proof in these cases has been resolved. Lord Hoffmann’s opinion in Re B has been relatively recently reiterated by the Supreme Court in Re S-B (Children) (Care Proceedings: Standard of Proof)  UKSC 17, and latter applied in the unreported case of Re D (Children) Court of Appeal (Civil Division) 17 October 2012.