Yes; you need to use the break clause and serve a section 21 notice to start eviction proceedings during a fixed term.
Quoting from Landlord Law Blog:
activating the break clause does not give you a legal right to possession of the property nor does it mean the tenant will have to leave.
A break clause 'breaks' the fixed term – but this will be followed automatically by a periodic tenancy. Which will have the same obligations and rights as the preceding fixed term. Meaning that your tenant still has a tenancy and is entitled to remain living in the property.
So, to recover possession (assuming the tenant is not going to move out voluntarily) you will need to get a court order
This applies to section 21 notices, which can't take effect until the fixed term has ended - but also applies to some section 8 notices, as certain grounds also can't be used during a fixed term.