Changing the Terms (Not Rent Only)
If the tenancy is a fixed-term assured shorthold tenancy, the landlord can only change the tenancy's terms within the fixed term if the tenant agrees. It is best to agree on any changes in writing.
Usually, any changes are made by getting the tenant to sign a new tenancy agreement, incorporating the new terms and conditions.
After the fixed term of an assured and assured shorthold tenancy has ended, a statutory or contractual periodic tenancy will arise on the same terms and conditions as the fixed-term tenancy. The 'period' will be the period for which rent was last paid under the fixed term, typically either weekly or monthly.
There is also a procedure whereby the landlord or the tenant can propose new terms, including a new rent which the landlord can do, within a year of a statutory periodic tenancy arising upon the fixed term ending, using a particular procedure under the Housing Act 1988. There is a specific form, called a section 6 notice, which the landlord must serve on the tenant. This procedure may include a change in rent (up or down) but should not be used to change the rent alone (for rent only changes, see section 13 notices later). Landlords can obtain the forms from landlord associations, law stationers or solicitors.
Although rarely exercised, the landlord and the tenant have the right to apply for an independent decision by a rent assessment committee if the new rent cannot be agreed upon.
The Difference Between Giving Consent and Changing Terms
In many cases, the terms of a tenancy agreement don't need to change to agree on something different because many terms in modern contracts won't outright prohibit some act but will instead only prohibit "without prior written consent".
A good example would be a tenant asking to have a pet or take in a lodger after the tenancy has started.
Pets
Most modern tenancy agreements will say that no pets are allowed without the landlord's prior written consent, which won't be unreasonably withheld.
Instead of changing the no pets term, the landlord can give consent if they wish, which is advantageous because the consent can be specific to exactly what permission is being provided for (e.g. one dog or one cat). The consent can also be subject to conditions.
Taking in a Lodger
Like pets, most agreements will prohibit sub-letting but may also allow for consent to be given.
The landlord could provide such consent to allow a temporary guest or for the tenant to take in a lodger. (In the case of a lodger, if the proposed lodger is to occupy long term, it may be good advice to grant a new tenancy in the new names rather than allowing them as a lodger).
Again, such consent wouldn't require a change of the terms of the actual tenancy agreement.
Providing Consent
Any consent given should be in writing. If communication by email has been ongoing, emailed consent will be acceptable.
Consent should be explicit about what is being consented to and the conditions to which the consent may be subject.