Tenant has moved out but I still need to 'evict' to gain possession

Possession - Section 8 and Section 21

Hello,
I don't know if this is Section 8 or 21, but this is the situation.  I hope someone can help me please.... 
My tenant had her rent paid in full by universal credit.
I've had notification from the Council Tax dept she was moving out 31/03.  She told me she was moving out 07/04.  However which ever it was she has not 'given up possession'.
My contact at the council offices in the Private Rent dept tells me that until my tenant "Gives up possession" I cannot take back control of my property.  He says I need to evict her (even though she's definitely been re housed and her new property's rent is being paid for by UC).

I don't know which was to turn.  
The thought of paying 6 months mortgage and the various costs that'll be incurred while the 'eviction' process takes place has hit me hard.
Can anyone help me please with suggestions of what to do next ? 

Thank you,
Zelda