There seems to be some fundamental misunderstanding around IR35. It does not cut or increase your tax or your NI burden. It is simply anti-avoidance tax legislation designed to tax 'disguised' employment appropriately. Equally, the regulations themselves i.e. the factors used to determine whether someone providing services through their PSC is a 'disguised employee' haven't changed in any way. What changed in April this year was the burden for determining employment status and, importantly, the liability associated with getting a determination wrong. It shifted from the service provider or 'employee' to the 'end client' or 'employer'. What that has meant is that employers now have to take it much more seriously and are obliged to carry out employment status determinations. If an individual providing services through a PSC is determined, following such assessment, to be an employee in all but name then they must be taxed as such and not have the tax advantages associated with providing services through a PSC (usually a limited company).
In other words, if HGV drivers are effectively employees then they will be expected to pay the right level of tax. That is not an increase to tax rate, NI rate or anything else. It does not oblige anyone to pay NI twice. It is also definitely not true to say that IR35 only has an impact on those in the higher tax brackets.