I know I’m not any of those universities but I did do an open day at Newcastle when I applied to come to university and they used to be number one for creative writing on the league tables (not sure if they still are this year).
So in terms of rankings Newcastle would be one for you to think about.
However, location-wise the three you’ve stated are all very far apart from each other so I guess it depends on where you live and how far you’re willing to travel. I’ve been to Newcastle and Birmingham a few times. For example, Newcastle is very north and can get very cold in winter, but it’s a gorgeous place with lots of scenery and is close to the ocean, whereas Birmingham is a more central city UK-wise and has more links to other cities via train networks. However, it can be quite intense from my own experience being in a bigger city like that. I myself strayed away from big city unis in favour of a smaller university because of my anxiety. It’s all up to preference really.
I’ve never been to Warwick so I feel I can’t make any comments.
Hope this helps,