Can I work part time prob 8 hrs a week and claim JSA?

Yes you can still claim but it makes it complicated. You have to declare the hours you are working and the amount you are being paid. This for council tax too. They then take the amount that you earn from the amount you are entitled to claim and give you the difference. I'm assuming that as you have a family to support you would be receiving more than the single persons £64 pw allowance.

You can claim JSA but they will take your earnings into account. You can also make a claim for housing benefit and council tax, aswell as child tax credits for any dependent children, if you haven't already. If you can get regular work for 16hours or more per week you would be entitled to working tax credits. These hours can either be worked just by you, or combined hours between yourself and your partner (if you have one). If you go www.direct.gov.uk they have an online benefits adviser. This can estimate amounts you may be entitled to. This includes housing benefit and council tax benefits.