I note Sumption (and Dignitas) refer to it as assisted Suicide.
Kim Leadbeater was asked about this and she said she was very offended that it was being called that as it was for adults and this was being compassionate.
From the research paper linked to earlier by @Slothtoes:
‘Assisted dying’ is a legal practice in some countries. Physician-assisted suicide, which licenses clinicians to prescribe lethal drugs for patients to self-ingest, is currently legal in all such legislatures. In addition, euthanasia, in which clinicians inject lethal drugs intravenously to end a patient’s life, is practiced in Belgium, Luxembourg, Canada, New Zealand, Spain, the Netherlands, some Australian states and Colombia.
It's assisted suicide, or, when a doctor administers the drugs, it's euthanasia. "Assisted dying" includes both of these. Why would Kim Leadbeater object to the term "assisted suicide"?