My view is that there are several levels at which income tax and NI could be integrated.

The collection and administration could be done at the same time, for example. This we mostly have already. The rules used (such as definitions of terms and thresholds used) could be harmonised. This is done to a small extent, but the differences cause a lot of problems.

The tax base could be harmonised, such that any item chargeable to Class 1 is taxable as employment income and vice versa; ditto Class 4 and self-employment income. Again, this is done to an extent but the differences cause disproportionate problems in administration compared to the benefits (if indeed there are any).