It's not clear: "You can get £92.05 per week Statutory Sick Pay (SSP) if you’re too ill to work. It’s paid by your employer for up to 28 weeks.
You need to qualify for SSP and have been off work sick for 4 or more days in a row (including non-working days)."
The difference is that CCBC will be signed up to the LGA sick pay scheme as follows:
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in addition to which some will have their own professional association negotiated sick pay scheme which will pay full pay for six months, then half pay for the following six months.
There are, however, swings and roundabouts in all this. Private industry practice varies significantly over time. Before 2000, for instance, private industry was offering exceptionally good pension schemes, often non-contributory and paying 2/3rds of annual salary. Many of those schemes have now gone, and those left have become contributory. Since 2008 pay and pensions in private industry have become far inferior on average to those offered by local and national government.
I do remember around the year 2000 civil servants enjoyed the best terms of service, with a non-contributory pension scheme and very generous sick pay. How or if that's changed I don't know.