Well, Public Funds include a range of state benefits that are given to people who qualify.
It would be wise to take a little time to do some self-research a little about these Public Funds. At least to know that they do not include all the different kinds benefit that can be claimed and made payable by the UK Government.
To really understand specifically what these Public Funds are, they are defined in paragraph 6 of the Immigration Rules.
To guide you with your research the Home Office has produced a leaflet that nicely explains what Public Funds you can and cannot claim if the visa condition applies to you. It also explains what will happen if you break the condition
That leaflet is called No Recourse To Public Funds
Take a good look at the table on page 6
There are many cases where you will not be able to make any claim for the benefits that count as public funds in your own name.
But, there are some claims that can be made in the name of your UK Citizen spouse/civil partner that will not count as recourse to public funds.
Child Benefit
The UK Citizen spouse/civil partner can claim Child Benefits in his own name.
See the HMRC booklet Child Benefit if you are coming from abroad or going abroad
Also see this leaflet called Child Benefit -Getting your claim right
Extract - "Who should claim Child Benefit?
You should fill in this claim form if you are responsible for a child. You do not need to be the parent of the child and you may be able to get Child Benefit even if the child does not live with you. Only one person can receive Child Benefit for a child."
Means stepchildren are included and can be claimed for.
Tax Credits
Tax credits were introduced in 2003, and the immigration rules were subsequently modified in 2005.
The rule change in 2005 affects couples where one partner is not subject to immigration control (eg. UK Citizen or permanent resident).
The rule addresses both working tax credits and child tax credits.
Under the rule, a couple may claim both these credits without jeopardizing any immigration status of the person subject to immigration control.
Means, a couple can claim child tax credits and/or working tax credits as long as one partner is a British citizen or otherwise exempt from immigration control.
When claiming any Tax Credit your UK citizen spouse/civil partner should tick the box for himself as the claimant.
Claims for Tax Credits are assessed jointly if you are living with a spouse or partner who is allowed to claim tax credits.
It will automatically be a joint application at the request of HMRC and your name will therefore appear. This is not a problem for you.
Here is some useful information from HMRC called What are Tax Credits and this page also has other useful links too.
Now, there are some other benefits such as, Contribution Based Jobseeker's Allowance, Housing Benefit and Council Tax benefit which although may technically be claimed under certain very specific conditions,
I would strongly suggest not to make any claims unless you are 100% certain of the appropriate legislation and can secure written confirmation of such from the legal teams of each concerned department.
In other words, even though it's technically possible (with knowledge of the legislation) it's safer to leave well alone until you have your hands on that ILR