Hopefully, the landlord will have a clause in the AST agreement that there will be an annual review of the rent. If so, write to the tenant(s) referring to the clause, stating that the rent will be £x from date. It is best to give at least two months’ notice of this.
Alternatively, the landlord and tenant could mutually agree a new rent. Then the landlord and tenant would sign two copies of a statement (normally a letter) stating the new rent, and when it commences. Both parties would sign both copies, and retain one each.
The best way of increasing the rent is serve a Section 13 notice on the tenant (Form 4) The tenant can appeal to the First Tier Tribunal before the new rent is due to commence.