I understand their point and I might even agree with it as long as the family was both paying for the health care and making the decision. But if the government is paying for the health care and/or making the decisions then I get very uncomfortable. And as this is in the U.K. it will be the government paying for the health care:

Doctors involved in childbirth are calling for an open discussion about the ethics of euthanasia for the sickest of newborn babies. The option to end the suffering of a severely damaged newborn baby - who might have been aborted if the parents had known earlier the extent of its disabilities and potential suffering - should be discussed, says the Royal College of Obstetricians and Gynaecologists in its evidence to an inquiry by the Nuffield Council on Bioethics, which examines ethical issues raised by new developments.

The reason I get concerned if the government is paying for it is that the health care budget is essentially fixed and to eliminating a few very expensive patients will save a lot of money. There will be a slippery slope they will have a great difficulty in avoiding. And once comfortable with elimination of those sort of expenses it will be more comfortable to "cut expenses" elsewhere. The elderly and the gravely, but perhaps not necessarily terminally, ill will likely find themselves next on the "chopping block". If the family is paying for it then there will still be financial pressure on the middle and low end of the economic scale but the option for the long shot attempt for a "normal" life will be available for some instead of being denied to all.