What an absolutely pointless statistical generalisation that report is. There is no hiding the fact that the lowest paid workers in the country are in the private sector; a combination of zero-hour contracts, contracting out of the lower paid manual workers from the public sector, jobs such as hospitality and agriculture being solely private sector based, and non-compliance with minimum wage legislation, all lead to this - but that doesn't mean the public sector is overpaid. This report also points out that the top paid x% are all in the private sector.
The key comparisons are 'like for like' jobs, particularly skilled professional 'technical' posts, and I suspect that there is at best parity, and more often than not a lower wage in the public sector.