Not in this case, as the UK's NHS is tax-payer funded.
There is more of an argument against taxpayer funds for the NHS than anything to do with sugar drinks in that observation. It is inescapably arbitrary what unhealthy behaviours are being subsidised vs. taxed.
That's because your observation is absurd and not grounded in reality. The reality is that obesity rates are too high in the UK. Most of these people overconsume sugary foods and overly processed foods. This in turn puts stress on the NHS, which affects all tax-payers in the UK so it's not a `strictly personal impact'. Overconsumption of sugar leads to measurably worse health outcomes than sitting in a field breathing pollen. The tax is not arbitrary.
High consumption of sugar is a worse problem than sedentary habits. “You can’t outrun a bad diet.”
On this specific topic someone drinking sugar drinks is clearly less harmful than someone smoking, because sugar drinks have a strictly personal impact. desiredState having or not having a different standard for tobacco doesn't cast a shadow on his opinions on sugar taxes.