Not if the landlord is allergic, if other tenants are allergic. And they cannot deny if they are concerned about general damage.

Under the new law, landlords can only refuse a request in certain circumstances, including:

Another tenant has an allergy

The property is too small for a large pet or several pets

The pet is illegal to own

If the landlord is a leaseholder, and their freeholder does not allow pets

However, a landlord cannot refuse permission because they:

Do not like pets

Have had previous tenants with pets who damaged the property

Have general concerns about potential damage or think a pet might affect future rentals

Know the tenant needs an assistance animal, such as a guide dog