Hey! First off, well done on sitting the TMUA—4.7 is still a solid score, especially since it’s a tricky test.
Regarding Imperial, it’s true that their typical TMUA scores are around 7, so your score is below their average. That said, your predicted grades of 3 A* and 1 A are really strong and can help your application stand out in other ways. It’s definitely worth applying if Imperial is your top choice, but make sure you have strong backups as well.
As for Warwick, they have accepted candidates with TMUA scores slightly below 5 before, so your score shouldn’t automatically rule you out. Again, your excellent predicted grades work in your favor.
If you want to strengthen your applications, focusing on your personal statement and references is key, and practicing some more TMUA-style questions could help if you decide to retake it. don’t be discouraged! Apply where you really want to go, but keep a balanced list so you have options. Good luck!