Of course any organisation needs to look hard at its cost structure.
And any politician needs to look hard at getting the next headline.
The advantage for observers when looking at the Civil Service is that they do publish wonderfully helpful statistics.
From the link below you can see that there are 7,860 Civil Servants in the HR profession making up 2.2% of the workforce. There are more civil servants working in security :-) (Page 18)
As you dig into the data more there are 9,580 people working in the HR function (including the professionals listed above) which takes the ratio up and makes up around 3% of the workforce
Is this number high? Well compared to the private sector probably as usually numbers quoted are around 1:80-1:150 rather than the 1:50 or 1:35 here. But the Civil Service have always managed people differently and taken a lead in certain areas driving core HR numbers up
assets.publishing.service.gov.uk/.../Statistical_bulletin_Civil_Service_Statistics_2021_V2.pdf
(as a foot note - 1,420 people whose profession is psychology - now that seems a lot!)