No pets 'ere, thank you very much ! It's not uncommon to see this in a lease or tenancy agreement. If you agree to it and the lessor or landlord hasn't gone on to say that you can ask for consent which won't be unreasonably withheld, then you are stuck with the prohibition.
Say the lessor or landlord has in fact agreed not to unreasonably withheld consent. Then they cannot act unreasonably. Saying 'no' to a herd of elephants in a two bedroomed flat would probably be more than reasonable.
The buyers of a flat in London's Limehouse were faced with a prohibition in the long lease they acquired in these terms:
No dog bird cat or other animal or reptile shall be kept...without the written consent...
Nothing about not unreasonably withholding it. That consent was needed from the development owners plus the management company. The buyers wanted consent for their young Yorkshire/Maltese terror Vinnie to live in the flat. The owners gave consent but not the management company. When Vinnie was installed the management company obtained a county court injunction compelling the buyers to remove the dog. The injunction was challenged by the buyers in the High Court which gave its judgment this week.
The majority of lessees in the development were against pets being kept there. And so the management company's policy was to refuse consent unless there were special reasons such as a guide dog being needed to live in. In this case, the buyers had said that they wanted Vinnie in their flat because the dog was part of the family and there were therapeutic reasons too for Vinnie's presence which would be supported by a medical report. Alas, that medical report never came.
A challenge to a 'no' decision where consent like this is needed can normally be mounted on the grounds that the refusal was effectively decided in advance or, to put it more dryly in lawyer-speak, on the grounds that the refusal was an illegitimate predetermination to reach a particular decision (and put that in your letter to your negative management company and tell them to insert it into their pipe and smoke it) and also that it was unreasonable or irrational.
But the High Court was having none of it. It ruled that it was implied that the management company would operate a reasonable process in deciding consent requests: but no more and no less. In considering requests, it had been quite reasonable to take account of a policy as set by a majority of the lessees that dogs would not be permitted unless there were special circumstances. That did not amount to an illegitimate predetermination.
The challenge failed and Vinnie must go.
The case is Victory Place Management Co Ltd v Kuehn and another  EWHC 132 (CH).