Affordable independence

I am looking to move to have my own space. I am an actor/artist/writer by training but I have a retail job to cover bills in the meantime. I have a small dog that would be relocating with me, he is an assistance dog. Ideally we would find one double room en-suite, but I am fine with sharing a bathroom, kitchen, living space, that has a washer and that the place is clean. I am quiet as far as flatmates go and I keep to myself as I don't get a lot of time to myself. I am usually busy, but I like to socialise and meet new people and explore London when I have the time. I would also need a little time to move in as I don't have a car to bring everything all at once.