HELP SAVE US BEING HOMELESS

Hello everyone my name is Jane and I live in London. I am 21 years old and have three lovely children ages 3 and a half, 2 & 2 months. I had stopped my job in April due to being heavily pregnant at the time, i was admitted to hospital early due to complications so was not able to make a housing benefit claim to help pay my rent therefore started to build up rent arrears :( Whilst in hospital I received a letter from my landlord saying that she has applied for possession of my small 2 bedroom flat this really caused me a load of stress as I wasn't in a position to be going out of hospital to get things sorted (although I really wanted to) Since having my child and getting out of hospital finally after a long time in there, I have got doctors notes, bank statements and everything I need to make a new claim for housing benefit. My landlord gave me 4 weeks until I have to leave the house so that housing benefit may backdate me to give me time to get a decision from them. I applied two weeks ago 04/09/2016 and just yesterday 23/09/2016 i got a letter from housing benefit claiming my reasons for not getting help before hand wasn't a good enough reason! I have asked my landlord if I can pay in instalments weekly or monthly but she is adiment that it needs to be a lump sum and I really cannot afford this with three children under four years old. The housing are claiming I've made Myself intentionality homeless and won't find me housing if we are kicked out unfortunately. I am here alone and don't have any family or friends here to ask for money or to stay with (I am really ashamed to be on here asking for money to be honest but it really is a last resort) I am really trying my best to fix this situation but it seams everyone is against me and no one is listening to my reasons. At the moment my rent arrears stand at around £5,500. Please could anyone with a good heart find it within themselves to help me and my family. I'm not asking for charity, please I am able to pay anyone back in weekly instalments. INSHALLAH SOMEONE OUT THERE WILL FIND US HELP I WOULD REALLY SINCERELY APPRECIATE ANY HELP. Thanks in advance to everyone that's taken the time to read this Jane, Jason, Yusuf and Layla :)