Social housing/eviction questioin - Bromley, London

I am an accidental landlord. My contract with the tenants(a couple with a baby) expired on 14th September. The couple got split up; the guy moved out on the last day of contract. But the lady and the baby still there in the property. She is getting help from social housing. The council asked me to serve section 21 notice which I did. Some people say that I have to apply for court order.
The lady is expecting financial help from the social housing.
Will it be too naive to expect the social housing to pay the rent? The lady thinks that they will pay but I have to wait until 1st November for the decision.
I am running out money; I don’t have rent guarantee insurance either!