You will be on UC regardless of whether your are in social housing or private rented. You seem to be thinking that you will be given a house and the rent paid for if it is social housing, let me dissuade you of this fallacious notion. YOU WILL BE ON UC REGARDLESS. It is an in and out of work benefit.
I've been there - I was given a eviction notice with a 9 month old when my private rental would not renew my contract for one in my name only even though i had been living there for those 9 months and paying the rent alone. I was on unpaid mat leave for the next 3 months.
I went on the list and bidded for properties i got informed of the private rental bond scheme. Fortunately for me my dad's acquaintance had just had a tenant leave a property they were renting out and i got in there even though half the floor was rubble. Some last minute luck there.
Back to UC if you are in social housing you will get the full amount of rent (minus any applicable spare bedroom rates and deduction for any non dependant person over 21) added to your entitlement. If private rent you will get 2 bedroom lha rate for your area or full rent if lower minus any over 21 non deps. Make sure you know what the lha is for you so you can factor it in when looking for the private rent. lha-direct.voa.gov.uk.
You need to face the fact you are very low priority, when i was bidding i was somewhere between 16 - 30 on the list, i am in the NW with a very short list in my area, still takes an average of a year to win on the bidded list.
Do not forget that you can get childcare costs reimbursed on UC up to 85% up to £646/Month. And you may still get UC top up as only 63% of after tax earnings over £287 are deducted from UC entitlement.