Section 21 or Section 8

Rent Arrears

We have a tenant who is almost 2 months in arrears. We have control of the rent from housing benefit now. We know that a Section 8 should be served for arrears situations but we believe she is hoarding money to move elsewhere. If this is the case -

1) Can we action Section 21b that was given and signed at the beginning of the tenancy? As we just want to get possession.
2) Do we then just have to write to say we are giving her two months notices under section 21b? Getting witness etc as you suggest and hand delivered and signed for.

We just want to get the property back in the quickest way as we don't think she wants to pay or stay.

he tenancy began on the 1/9/12 -28/2/13 and rent is paid monthly. The notice can be given after the 28/2/13 .