The offer of a telephone call comes out automatically. It’s optional. You can just decline it.
You are not on the tenancy agreement, the council refused to put you on the tenancy agreement and as your partner was the tenant and is now moved out, you have no right to remain in the property regardless of how long you have been the property.
It would have been different if you had been married to your partner but it appears that you are married to someone else.
In effect, by remaining in the property with your wife, your ex-partner who is the sole tenant’s is illegally subletting to you and that is a criminal offence so it’s actually more serious than you are probably thinking although it may be that the local authority are not particularly interested in pursuing that issue.
If you are being made homeless, and you have dependent children under 18, the local authority are under a duty to provide a home for those children And therefore you need to speak to the Housing Department and Social services.
It might sound rather strange that they are making you homeless in one respect but then under a duty to provide accommodation for your children and the family but that’s the way the system works.