probably not the best advice but in the past I have just not declared having a pet after struggling to find a pet friendly flat. then I just made sure i kept the flat clean and hid all evidence of a pet during inspections. it's not ideal but it's an option.
you could also offer to pay a higher deposit or a "pet deposit" if landlords are concerned about potential damage. Depending on the landlord that gesture of responsibility might be enough to persuade them |