Single Parent and public Funds

I am recently split with my husband (I do not want to start legal battle separation/divorce yet with a hope that he may comeback)..

i 've got 2 children’s 4 and 7 year old and i am not working at all ....
Children father is paying 1000 out of his 2000 net salary every month and he is living separately...

This 1000 is not enough as our expenses are around 1700 and now I am left with no saving at all..(I am paying 900 for Flat rent and 100 for council tax (after single person discount))

I have got ILR

My question are..

• If I apply for benefits how my application will be dealt
In order to be considered single mum do I need to be legally separated..?
• What benefits I can apply?

Please help me where I stand and what options I have got

Many thanks