I've just read, in the 'New Humanist', a review of a book called 'O, Let Me Not Get Alzheimer's, Sweet Heaven!', by a retired medical doctor called Colin Brewer, which discusses this issue. The difference between the two, as I understand it, is who performs the final act: if a doctor gives a patient a lethal drug, and the patient swallows it, that's assisted suicide, but if the doctor injects the lethal drug into the patient's vein, that's euthanasia. If life support is withdrawn at the patient's request, and the patient is an adult who is mentally capable, that is neither, and is already legal in the UK. I stand to be corrected on the preceding, provided the correcter knows what they're talking about, and provides evidence.
The review discusses the argument made by opposers that vulnerable people may be pressurised into requesting euthanasia or assisted suicide, but says that there is very little evidence from countries and regions that have already legalised it that that happens, and makes the interesting point that pressure in the opposite direction may also happen: people who'd rather be dead being pressurised to hang on to the bitter end.
It also seems to me that many opponents argue dishonestly; they come out with the argument just mentioned, because they know ordinary people are more likely to be persuaded by seemingly pragmatic, utilitarian arguments, but the real reason for their opposition is religious.
OK, let the argy-bargy begin.