Private and Public pensions (not including civil service pensions) are operated similarly to private pensions, i.e. funded from contributions and invested to realise the funds (in the form of interest and dividends) to pay pensions. There is no 'public' contribution 'to top' up the fund. Only the contributions paid during the employees service, which is continually invested.
Civil Service pensions are different and paid by the government from taxation.
Guides outlining good practice for academy trusts' in financial management and assurance.
www.gov.uk