Social or Council housing Spouse on Immigration control

[zzzindagi]

Hi Guys,

I have just received my ILR on 10 years basis.... My wife is still on Tier 1 Dependent visa..
MN1 application for my Two Children under process.

I have following questions please?

Is applying Social housing through housing register is a Benefit ?

I was filling up application forms on line and in the assessment form ( HED) when they asked about number of people in my family. I just entered 3. Myself and my two children and did not include my wife considering that she is under immigration control.

But on the Application form (Housing Register) they again asked about the Household members. In the Terms and Conditions they warned that the person giving them false information or hiding any kind of information will be prosecuted.
Now i am confused whether i should put my wife's name in the household members or not.
If i put my wife's name in the application form then she might be breaching the conditions of her visa and if i don't put her name in the form the council may think that I am hiding or giving them false information.

Can any senior member please advise what should I do.. ?

Many Thanks in Advance