It is very unlikely that they would evict you as that would make you homeless and therefore in priority need on the basis that you have 4 children.The local authority have a duty to help the homeless, if you did not have the children then of course this would be a different matter. the best strategy would be to continue to pay off the rent arrears as quick as you can with out spiralling into further debt.(posted 7358 days ago)When it is reduced this should make you fairly secure. However one would need to see the possession order and whether or not that the order is or is not a suspended possession order, if it is the latter it would be very unlikely that you would be removed from your current home as you are paying towards the arrears which is all what the court wants.
Most certainly you need to get down the local Citizens Advice Bureau, they are quite used to this sort of thing and would be able to help with, as stated abouve with Benefits, Housing Benefit, Council Tax benefit. Remember you do not need to be on Benefits to receive this, especialy if your on a low income with yourself or partner working, which is when one should start to look at whether or not you are receiving the correct amount of Working Tax Credit/Child Tax Credit.
Good luck
Justask