Despite how it’s often framed, the NHS doesn’t get to make recommendations one way or the other in this kind of case. Once the patient’s doctors are no longer sure that it’s in their best interest to continue being kept alive, they make the legal system aware, and a court will take evidence from the patient (if they’re in a fit condition to give any, which they usually wouldn’t be), doctors, family members, relevant experts, and any other appropriate witnesses, to determine what is and isn’t in the patient’s best interest. One the court has made a decision (which might involve a lengthy appeals process if the family are upset about the initial decision), the NHS does what the court tells it to. If the patient is capable of experiencing anything other than pain, it’s unlikely that it’ll be in their best interest to die, so the court will order them to be kept alive.

It’s relatively common for anti-abortion and anti-state-funded-healthcare political campaign groups from the US to pay for expensive lawyers to argue in favour of keeping child patients alive and persuade the parents to keep appealing as upset parents saying the state killed their baby makes an evocative headline that can easily be pivoted to make the most merciful option look cruel and callous, and sway people’s votes.

There’s a chapter on this in one of The Secret Barrister’s books - I think the second one.