The problem you're missing is they're trying to find an alternative, aka Italy is willing to shoulder this problem and take it upon themselves, but Britain declines. The broken part is the continuum of care. It is common practice to comprehensively treat acute conditions and transfer patients through rehabilitation processes and the like so that additional acute hospital admissions do not happen. This ends up cutting costs long-term and doctors know this. Additionally, they took an oath, as is required for all doctors to take, to willingly do no harm. But where the ethical part plays, is that besides violating that oath, administration would have passed down the order to take the child off life support for doctors to pull the plug without consulting or getting the consent of the parents.
Britain declined transporting the braindead child themselves because of citizenship issues as well as resource issues. Since everything is paid for by the government, they have the final say in whether they choose to dedicate resources to granting the child full citizenship as well as airlifting them out.
The child's brain death isn't an acute condition, its a chronic and degenerative disease that is guaranteed to kill the child at a certain point in its life (probably within a few years). The hospital decided that they could no longer dedicate the resources to keep the child on life support. The parents are able to transfer the child to a different hospital if they want. There's nothing immoral about it, and it doesn't violate their oath. Keeping terminally ill patients on life support indefinitely costs much needed resources that could be use to treat patients with actual acute conditions.
Hospital care costs money, and that money has to come from somewhere. Life support is incredibly expensive, eventually there has to be a point when it can no longer be sustained, and a decision has to be made.
