This is a pretty complex calculation, and there are some wildly different numbers floating around. Anti-smoking campaign groups clearly want to make them as high as possible but on the face of it not everything they say is entirely convincing.
For example ASH claim that "Smoking costs England £49.2 billion each year in lost productivity and service costs, plus an additional £25.9 billion lost quality adjusted life years due to premature death from smoking."
But some of their numbers seem debatable. For instance, they say that the "cost of informal care by family and friends" incurred by smoking is £8.4 billion per year, and that the cost of "unmet care needs" is £5.4 billion. I'd be interested to know how numbers like that are calculated, and also in what sense an unmet care need is considered a cost.
They've also claimed that the UK economy is a whopping £13 billion worse off because people are spending money on fags rather than on other things, and magicked up a lot more billions by apparently assuming that people whose unemployment is "smoking related" would be in employment if they didn't smoke.
It may be that they have robust methods of calculating all these numbers, but if so, I can't find any description of them.