What Wanderer has said on Child Benefit is spot on. If one parent is on ILR then it can be claimed.
Maternity allowance and statutory maternity pay are different.
People on spousal visas/FLR/Leave to enter/people not considered settled for the purpose of the immigration rules are entitled to contributory benefits, which are NOT public funds, although some may depend on the amount of NI contributions made.
This document is from 2005, but I believe it is still accurate
http://www.ind.homeoffice.gov.uk/docume ... iew=Binary
So, statutory maternity pay would not be considered a public fund.
Maternity Allowance is only paid to those who do not qualify for SMP. It is also a contributory benefit, so you have to have been working for a certain amount of time in the UK or a country with a reciprocal agreement to qualify. It is also not a public fund. This page might help:
http://search2.openobjects.com/kbroker/ ... +allowance
Victoria