Need to regin possession now in PERIODIC TENANCY

Possession - Section 8 and Section 21

Hi

I have a tenant that has gone into rent arrears and I would like her to leave. She had a 6 month AST and also signed a Section 21(b) at the beginning of the 6 month period. So here we are in month 7 and she has dropped onto the PERIODIC TENANCY. According to the RLA:

"The 2nd set of rules covers the SERVICE of the notice AFTER the tenancy agreement has ended. The Landlord has never served a S21 notice before. If he has, he can rely on the earlier notice."

So as she signed the S21(b) does that mean I do not need to serve a S21(a)? If I don't need to, do I simply write to her stating she has 2 calendar months to leave. Is there a standard temple letter?

Many thanks

James