Hello, I am a solicitor with 20 years experience. I will try to help you with this.
It will be a breach of contract for you to allow more than one pet if the agreement states "a cat/dog". However if your labdlord is aware that you have 2 dogs and has been for some time and done nothing about it then there is certainly an argument that he has agreed to waive this clause. What sort of tenancy do you have is the landlord an institution or an individual?. Isther an allegation of nuisance by the animals?
I will be off line for a while now but will look again later.
The agreement does state "a dog/cat" and further on states "the dog and the cat will not be a nuisance...." I have 2 dogs and one cat and thought the language was not specific, i.e. there is no such thing as a "dog/cat" and that it did not state 1 of each is allowed, just used "the" and I thought that it implied that pets of the dog and cat nature are allowed, and not explicit in only allowing 1 of each. The landlord is in an individual and I remember a conversation before the tenancy started 3 years ago about my pets so he has always known. There is no issue at this time I just wanted to know my position if it becomes an issue. Your response is helpful, thank you.