Do coroners have the power to reject a Cause of Death?
I suppose the short answer is "essentially yes" although, in practice, but it i "not really like that", not the least because they will often/usually 'not get a chance' to reject it.
• If an attending doctor feels able to 'certify' an explicit (and 'acceptable') Cause of Death, then the Registrar will virtually always accept it and record the death, and issue a Death Certificate, accordingly. That is by far the most common situation. A coroner is not involved in that process at all (unless, I suppose, someone 'complains' by themselves involving a coroner).
• If there is no appropriate doctor, or if no attending doctor feels able to provide an explicit (and 'acceptable') Cause of Death, the case will be referred to the local coroner. The coroner will then arrange for an autopsy to be performed and will then (after seeing autopsy report) themselves report the Cause of Death to the Registrar (who will then record the death and issue a Death Certificate accordingly). If, as nearly always is the case (although perhaps it shouldn't be, per my previous comments!), the pathologist provides an explicit (and 'acceptable') Cause of Death, the coroner will nearly always accept it. If not, it is for the coroner to make the ultimate decision, which may require an Inquest to be held, and that decision might, sometimes, amount to 'rejecting' the pathologist's conclusion.
• If an attending doctor provides a Cause of Death which is 'unacceptable' (or of doubtful credibility), the Registrar will report the death to the coroner, who will then proceed as in the previous paragraph. It is therefore really the Registrar who will be the primary person doing the 'rejecting', although they will almost always make the same decision as a coroner would have made.
• There are rules (sometimes 'local' ones) regarding deaths which must be at least 'discussed' with the coroner (in practice, a "Coroner's Officer", usually a specialised police officer) - e.g. those occurring within the first 24 (sometimes 48) hours after admission to hospital. These discussions may lead to the coroner 'taking over the case' (as in second bullet point above) but, if the situation is straightforward, permission will often be given for the attending doctor to certify' the Cause of Death - e.g. if someone dies within minutes or hours of being admitted to hospital with a 'proven' heart attack or stroke.
• There are also cases where deaths have to be dealt with entirely by a coroner, usually requiring an Inquest - e.g. traumatic deaths, 'suspicious' deaths (e.g. possibly due to homicide, criminal negligence/neglect etc.) or when 'occupational factors' may have contributed to the death.