S21(1)(b) and break clause options

Tenancy Types and Management

My tenants have given in writing, two months notice to terminate our tenancy agreement, using the 6month break clause which had been written in to the AST. I agreed to the termination in writing.These tenants then asked if they could change their minds and have a further two month extension beyond the original termination date of their AST . I had to say no because I had already advertised the property and arranged viewings. I have now accepted a deposit from new tenants and I have issued a pre-tenancy agreement subject to contract. What would happen if the original tenants refused to leave on the agreed date? I had already issued the S21(1)(b) at the start of the tenancy. Do I have to issue another notice or do anything else to make the early departure enforceable in law?