Thanks for your response
Then you may have a claim for child tax credits, for the 13 year old stepdaughter IF there is a valid claim for child benefit which might require you to make this claim as your partner is not eligible for UK benefits.
Council tax - yes, you can make a claim to your local council for this, and get 100% reduction. But there are no other help other than that which the school might offer for school trips, and free school meals.
If you have interviews then there is assistance with travel costs, and purchase of suitable clothing such as a suit, but not general help with travel, or clothing, plus through DWP (Jobseekers) there is what was known as the social fund which provides assistance with household items or emergency situations. However the social fund was abolished in April 2013 and each council may or may not participate in the new arrangements, and this is something you will need to ask your local Jobcentre.
Then there are food banks, which are becoming more in demand and are springing up everywhere, and you would qualify for assistance here too.
Free courses in Adult Education, for GCSEs and some other social courses.
Other than that, I am afraid there is not much more I can think of (as most of this is not mainstream assistance), I'm sorry there is not more available, as I know what a struggle it can be.