Many owners of rental houses, in fact, most of them do not allow pets in their rentals and it is not always a good attitude
In the article entitled "Pet-Friendly for Whom? An Analysis of Pet Fees in Texas Rental Housing" published at https://doi.org/10.3389/fvets.2021.767149 its authors make an analysis with interesting points regarding the presence of pets in rental houses" these are:
Pet Friendly Rentals
On the other hand on the website https://www.simplybusiness.co.uk, Jade Wimbledon comments about Pet Friendly Rentals says:
"...In the UK it's raining cats and dogs The country is full of pet lovers, with around 16 million dogs and cats living in British homes, not to mention the rabbits, fish, birds, hamsters and other critters that share our space."
BENEFITS OF PET FRIENDLY by HOMEOWNERS:She explains reasons to allow pets in your rental and be a Pet Friendly Rentals, among which she mentions:
Pet Friendly Rentals / Florida Keys rentals
by Ellis&Co at https://www.ellisandco.co.uk/news/renting-with-pets-london
There are no specific laws in place when it comes to renting with pets.
Ultimately, landlords can decline requests from tenants to keep a pet if they have a valid reason to do so.
Your landlord, therefore, could decline your request if:
Pet Friendly Rentals / Florida Keys rentals