Grad student and pets ISO place to live

Hello! I am going to be moving to the UK to attend the University of York as a graduate student this September. I come with both a dog and a cat who are both extremely friendly (pictures included) so any roommate/accommodation would need to be pet-friendly.

Juliet and Mr. Wimby are both great with other cats, but Juliet was a Covid-puppy who didn't have the chance to socialize with other dogs much, so she doesn't respond well to dogs unfortunately.

I have preferences for the room/apartment I'm looking for but they are not deal breakers. I would like to find a double bedroom with a private bath that is ideally furnished but aren't necessary.