CAN A LANDLORD VARY A LEASE JUST BY SERVING A NOTICE OF VARIATION UPON THEIR TENANT,

The answer is likely to be NO.

Under the Unfair Terms in Consumer Contracts Regulations 1999 a landlord may be not be able to  vary a  tenancy just by giving his/her tenant notice.  A Landord's best course of action would be to  attempt to agree a variation with their tenant. If the tenancy is a long tenancy, a Landlord may wish to consider whether he/she can apply for a variation under Part IV of the Landlord and Tenant Act 1987.  Detailed advice in respect of these provisions may need to be obtained.