As the above poster said, you should go to the CWO and apply for Supplementary Welfare Allowance. There is a technicality that you must have exhausted all other possible payments before you apply for this, although previously someone in your circumstances waiting for the three month period didn't pose a problem and CWOs would have generally paid up, but they are tightening up all over the place.
If your CWO is being difficult, best thing to do would be to apply for Jobseekers, and then you have at least applied and are in the system, and there shouldn't be a problem applying for SWA from your CWO while that claim is processed. Then when the three months is up, you can apply for OPFP.
While you are applying for or receiving Jobseekers (and SWA pending an application for Jobseekers) you will have to demonstrate that you are seeking and available for full-time work. Although once you get to the 3 month point, and switch over to OPFP, this no longer applies.
What age are your kids? Just to let you know in case you didn't that from 27th April OPFP for new claimants is only payable until the youngest child turns 14 (although if the youngest child is under 14, you still get an increase for any other child up to 18 or 22 in f/t education)