I don't think it is necessarily the fault of the NHS, this is generally the culture in this country. Because we have only SSP as a safety net for people who are ill, many people simply can't afford to take time off when they are.
What we need is twofold. Firstly SSP needs to be improved to match at the very least minimum wage, and preferably backed up with employer contributions to make anything up to 100% wage for illnesses like covid & flu. This would need to go hand in hand with some level of testing so that employees don't take the proverbial & provide them with evidence so that employers don't do the same. And secondly employers need to learn to build in contingencies for such things, ensuring that they don't unnecessarily pressure staff into working when they shouldn't and to plan for at least some level of sickness especially during winter.
Of course all this would come at a cost initially, but by giving more support to people who need it, you reduce the transmission of illnesses, and in time improve staff moral & confidence, improve productivity & ultimately profitability. What we must not do is go down the route of countries like Japan & hide the problem away behind masks. Countries like that may seem more disciplined, but underneath that seemingly pragmatic approach is people being overworked, working when they shouldn't, and sadly a very high level of unhappiness, depression and even suicide. If we must define a "new normal" it should be around a better approach to work / life balance, not adding more restrictions to give the impression of normality.