The impact of a tobacco levy on the tobacco market would be similar to a duty rise, with tobacco manufacturers and importers passing the levy onto consumer prices.
As tobacco duties have already increased this year and will continue to increase by more than inflation each year in this Parliament, the government has decided not to introduce a levy on tobacco manufacturers and importers
Feel free to contradict me in the comments, but my understanding of the issue is this:
ASH's original idea was to have a literal levy, like a windfall tax or the Master Settlement Agreement, in which companies would have a certain proportion of their profits taken from them by the government.
This was never practical because the British government has no authority to take profits from companies based abroad (eg. JTI and PMI) and the companies that are still based in UK (BAT and Imperial) would be sorely tempted to up sticks if such a levy came in.
In the last budget statement, the government noted that its public consultation had identified some problems with the idea of a levy. By the time I was debating this on the radio a few weeks ago, ASH seemed to have come to terms with the fact that it was impractical. Instead, they were arguing that an additional tax be placed on tobacco, the proceeds of which would be ear-marked for anti-smoking initiatives, ie. for them and their mates.
This amounts to no more than an additional sin tax on tobacco, with the usual negative impact on the poor and on the black market. Since tobacco duty is already due to rise above inflation, with the money going towards general government expenditure rather than prohibitionist pressure groups, the government has decided to call the whole thing off.
Good. Now the government needs to stop funding ASH entirely.