A blanket ban is much more reasonable in the UK where health care is publicly funded than in some place like the US. Someone may think they deserve the right to smoke if they feel like it, but that doesn't go well with the idea that someone should also get healthcare for free when their bad decision results in the natural health consequences.
Banning something that's highly addictive is almost certainly going to lead to a black market. But, maybe that's better than the alternative? It doesn't sound like it though. Australia's cigarette black market has not only resulted in black market cigarettes, it has also resulted in gang wars over territory to sell those illegal cigarettes.
It seems to me like high taxes are a better idea. If someone wants to kill themselves slowly and inconvenience anybody around them while they indulge their disgusting addiction, make them pay everybody for that privilege. But, if it's just super high taxes, that's also going to result in a black market. Apparently in the UK nearly 90% of the cost of a cigarette is taxes already. Maybe they could have an effect with different tax levels for different ways of obtaining cigarettes. For example, a convenience store could have the highest tax rates, serving people who were truly desperate. Or, you could order from a heavily regulated delivery retailer that would deliver a monthly supply. Maybe a low-ish tax rate if you were ordering only 20 cigarettes per month through this site, and a high rate if you were ordering 60+, but not as high as the corner store rate. That would encourage people to keep their consumption low, and discourage them from buying extra cigarettes on top of their regular monthly supply.
A ban doesn't sound like it will work. In particular a ban that only affects some people based on a lottery on when they were born. Especially if that lottery means they'll never legally be able to do something that someone born days earlier who might be part of their friend group can legally do. I don't think that's ever going to work out. If they wanted to ramp up the age, it would make sense to either make it slower or faster. If it were slower, (like, people born in 2008 could legally start smoking at 20, 2010 -> 21, 2011 -> 22, etc.) then people might decide to follow the law and then realize that they don't actually want to smoke when their year comes up. Or make it faster so at first it's people born in 2008 and after who can't legally smoke, then people born in 2005 or earlier, then 2000 or earlier. If you're a smoker and you want to avoid that ban, you'll know it's coming and have time to try to quit before your year rolls around. Then it's not just generation 2008 that has fewer rights, it's just that their year came up first.