Short answer: look at the websites of the universities you want to apply to, it will specify there.
Long answer: You can only take MAT if applying to Oxford (required), Imperial (required if applying before MAT registration deadline), or Warwick (not required - you have to take one test, but you can choose), and if you do take it you can also share you result with Durham and/or Bath.
Anyone can take TMUA, a large range of universities use it but as far as I know none require it. Many will give a lower offer if you do well enough in it.
Anyone can take STEP, which is required for Cambridge, and some others use it similarly to the TMUA.
I don't know about AEA but I imagine it is similar to TMUA.
MAT/TMUA are done in October 2023, STEP/AEA in June 2024.