Lots of good advice here, and I agree with almost all of it (except for the use of polarising filters which cut out too much light - particularly as the lighting is not very bright at Birmingham).
I recommend that you have a good look at the photos taken there in our Gallery: you will see that the most recent are the ones I took last year. I found that I had to use higher ISO settings than I normally choose because the lighting in many places is quite dim - but I was prepared to do what was necessary to get a photo if it was possible.
The first exhibit with the gentoo penguins is actually one of the brightest, so make the most of it

Then you work your way up the building past a wide variety of pools and tanks: each one has its own challenges and I found that it was impossible to get worthwhile images in some of them with my equipment.
I am sure you will want to take photos of the sea otters at the top of the building. It isn't easy. The spotlights seem very bright, until you actually try to use your camera and find that they are not nearly as bright as they seem - but they are very contrasty, which makes things difficult. Adjust your camera for low contrast if you can. For more details look at my post
Sea Otters at Sea Life Birmingham [SEA LIFE Birmingham]
For the sharks, rays, guitarfishes and the turtle in the main tank, I found that the widest angle setting of my zoom lens was the most useful. I could not get any decent photos through the curved plastic of the tunnel through the tank; I took all my photos through the flat windows by the stairs and the lift at the start of the tunnel and round the corner from the penguin window by the entrance to the gift shop.
Enjoy your visit!