There is already taxation on cigarettes and alcohol: in 2010, ASH claimed that 'The UK tax paid tobacco market is worth around £14 billion health related costs £5 billion)'; Revenue & Customs state that in 2009/2010, £9 billion was raised from alcohol sales (couldn't find health related costs), 'around 2% of the Government’s total revenue from taxation.' I'm not sure how much tax you could put on sugary things without it seriously harming many industries and creating more unemployment.
Information from The NHS Confederation states that the NHS has annual running costs of £105.254bnf but the NHS Choices website states that it receives a budget of [for 2012/13] 'it is around £108.9 billion' - so I'm a bit confused (but any mathematical stuff will confuse me).
Overall, compared with other countries and their version of the NHS, we do quite well.
I feel that the problem with the NHS is that it tries to be all things to all people and, if money was no object, that ethos would work. Money is a problem though and maybe the NHS needs to go back to dealing only with medical problems and only offer 'cosmetic' treatments where an adverse effect on health of a person is evident. Everything else could carry a cost contribution (which would, imo, be better than taxing everyone) that isn't covered by existing taxation (so I would exempt smokers and drinkers as they are already contributing to the NHS). I tried to find what ailment costs the most annually but couldn't find it.
I agree with others that it should be a 7 day week for the NHS, it doesn't make sense to have equipment sitting idle for two days every week.