Ironically banning them probably goes against the Conservative ideology even more than what we do now (taxing them considerably), so can hardly see even his own party backing this. They'd probably get a similar outcome without potentially creating (as many) black markets for them by just taxing them more.
20% is a huge risk of cancer. Compare to cervical cancer, which considers that those who don't have an HPV vaccine or get screened have a 1-2% lifetime chance of developing it, and it's considered a very common (WHO estimates it as the 4th most common for those with a cervix) cancer. Hand waving it that 1 in 5 smokers getting lung cancer is absurd - that's literally 10x more common than cervical cancer which is such a big risk the government has made cervical screening available to all those who may be affected over a certain age as I understand
Also smoking invariably exposes others and not just the smoker, so it's a double dip health risk. People smoking not only put themsleves at risk, but also others. And even if they did "only" put themselves at risk, that represents a significant taxpayer cost in treating them, not to mention potential social care costs, employment related costs/opportunity costs, etc. It costs everyone. There's a reason it's a major focus of public health initiatives - not only can cutting down on smoking and associated cancers save lives, it can also save a lot of money that could in theory be used to support other health or social care initiatives or public services in general.
Also nicotine isn't an additive it's a naturally occurring chemical in tobacco plants. Removing it is probably a lot more complex than you are implying, if even possible.