despite the budget for the NHS being almost half of our total spending in the UK

I don’t think that’s true - wherever you saw this, it was probably combining health with ‘social protection’ (i.e. pensions and welfare), which is the single largest spending category - all combined they must equal about half of central government spending (or about two-fifths of total once you factor in local government spending).

But I think you are alluding to an important point - health spending has been consistently growing for decades (in nominal terms, in real terms, or as a share of government spending), and despite this people’s experience of the NHS is deteriorating. Health was around 8% of government spending in the 1950s and 60s, rising to 10% in the 1980s (when it overtook defence), to around 16% in the late 2000s, and continued to grow to around 18-19% going into Covid.

I think part of that is about growing demands on the NHS from a population that is older and generally a lot less healthy (looking at overweight and obesity figures - a driver of many common health problems like cardiovascular disease or many cancers). But part of it is also about political mismanagement, political tinkering and change fatigue in the NHS.

‘Privatisation’ is a dirty word in UK health politics, but I do increasingly wonder if a model that takes the delivery of healthcare outside of political control - i.e. turning the NHS into a buyer of healthcare on behalf of the public, analogous to how public health insurance works in many European countries - might be a better model to protect healthcare providers from the incessant tinkering and legions of management consultants that have come with political control under both Labour and Tory governments.