Set M application Housing Register

[Sag A Little]

Dear Members,
I have a question whether Housing Register will affect my current Set M application.

I have applied for ILR in September 2018 on a 5 year partner route.
In 2012 a judge granted discretionary leave to remain as a partner on Human right basis.( I was married previously in 2007 and divorced in 2009 due to crime and domestic violence. However home office did not treat it as sufficient.)

Long story... My partner is ILR holder based on Tier 1? since 2013, we have 2 British boys since 2014.
I have a job, he has a job, our combined income over 32000£. He claims child benefit.

In August we were affected by a landlord's decision to sell the house. We were paying rent on time. But he served section 23 notice and he can start eviction process anytime.

My problem is- I sent an Ilr application, but we can not move into a private rented house because my partner has CCJ on his name due to a fraud in 2013. In 2013 my partner lost over 25000£ because he had to pay the bills acquired by a different company on his name. We won the case in 2014 but no one was able to return the money.
This CCJ prevents and will prevent us from future private renting. We physically have to go on council housing register otherwise we will live in a tent.
Will this registration affect my Ilr application?
I think Yes, it will, but we have no choice really. And, if I will be refused ILR, and move back to home country, my partner will claim more benefits as a single father.

Any advice appreciated.
xxx

[Sag A Little]

Forgot to mention I have a NO RECOURSE TO PUBLIC FUNDS on BRP.

but since the situation is difficult I am ready to go back home for my partner and kids get a council house, as it is essential and inevitable for the future.