It seems to me that the hospital authorities see this as a matter of professional authority and ownership of the case. The expression "release that case to another hospital" is a fair expression of that way of thinking. There are contexts where that can have its validity. Professional and even institutional expertise is important and deserves to be respected. But it has its limits.

A flight to Rome would involve a journey time comparable to many hospital transfers within the UK. If it turned out that Alfie was unable to survive the journey, the outcome would be the same as is in any way predicted. If support procedures which have been withdrawn were renewed for the journey the chance of his surviving it would presumably be greater.

As for "the mob", the kind of inappropriate behaviour reported is very similar to what has been reported in other protests where issues of human rights and human life are involved. It is also customary for this behaviour to be used to shift the focus from the actual issues involved - for a contemporary example consider Trump's spin on Black Lives Matter. Personally I remember the same in the same tactic being deployed in face of Vietnam protests, and many other times.