This is an excellent example of how the slippery slope is real. This 2006 article discusses statements by the Ethics Committee of the Royal College of Obstetricians and Gynaecologists (RCOG) pertaining to euthanasia for severely-ill new-born babies.
In a 2005 memorandum, the RCOG urges the Nuffield Council on Bioethics “to think more radically about non-resuscitation, withdrawal-of-treatment decisions, the best-interests test and active euthanasia as they are means of widening the management options available to the sickest of the newborn.” The memorandum also discusses economics, presenting them as a legitimate element of consideration.