The argument for this is a simple one of efficiency. For the same amount of taxing, the government could spend more (or reduce the deficit) and business in the UK would become more efficient with less work required to do its payrolls.
Currently we have these two systems of tax which are similar in many ways. As no tax is hypothecated, the argument that NI is for certain uses is bogus. Clearly, if we just had income tax on all types of income in would be more efficient to collect for both the government and business. Although this would be a radical step, people aren’t stupid and they would clearly see that the overall tax take was the same.