So based on the BMA guidance, the courts may therefore consider an older child's consent to circumcision to be valid so long as the courts think that there has been no undue parental pressure and it is the child's own choice.
Yes - but why are you focussing on circumcision which is a rather unusual medical procedure as in most cases there is no medical reason for it to happen, in other words is non therapeutic. There are also oddities in relation to parental 'consent' or authorisation. In most cases the agreement from one person with parental responsibility is sufficient for authorising a medical procedure. Non therapeutic circumcision requires authorisation from both parents. So in effect each parent has a veto. The only other circumstance where consent is required from both parents is within the world of assisted reproduction where both parents are required to consent to the generation of embryos by IVF and must both consent to future use, storage etc.
So a child is capable of making their own choice under current thinking.
It is a little bit more complicated as you need to consider both the ethical principles of consent and the legal position.
So if a child has capacity to consent (so-called Gillick competent), is provided with sufficient and adequate information and is permitted to make a choice free from undue pressure etc, then that is valid consent. However that doesn't mean that legally that child is permitted by law to engage in certain activities even if all the conditions for valid consent are met.
So perhaps the most obvious example is sex - while it is perfectly possible, under the ethical principles for people aged under 16 to provide valid consent, if the conditions above are met, this is still unlawful.
Other examples are blood donation (age 17) and tattoos (age 18).
Of course all of those things would be unlawful without consent at any age.
So you need to look at both the ethics of consent and the law to determine whether something is actually lawful.