The Parliament of the United Kingdom has looked at this issue quite a few times over the last 20 years. They had a parliamentary committee study the issue in the mid-2000s, I believe.
They also recently had something akin to a private member's bill that was debated and was defeated I believe in September of last year. One of the interesting features of that legislation is that it would have adopted a model quite close to the U.S. state model, which is physician-assisted suicide only and only where the person is terminally ill and facing death in the short term.
One of the interesting things about the U.K. legislation is that they clearly were just uncomfortable with the idea. In the U.S. models, the patient receives the prescription, which they then take home. About one third of patients don't ever take it. About two-thirds do, but they're able to take it whenever they feel the need.
I think the U.K. Parliament was troubled by the prospect of those drugs being available to the person, perhaps to take at a time when they were not competent. They developed a process whereby the medication would only be delivered to the person at the time when they were going to take it. They would always be in the presence of a medical professional. If they decided not to take it after it had been delivered, then the drugs would be removed by the medical professional. They could always be brought to the patient again on another occasion.
That's an interesting thing to look at if you're interested in this area, because it does provide a model for a supervised physician-assisted suicide regime.