If I am applying to courses at both Imperial and Cambridge, do I need to take the same test more than once?

You only need to sit the relevant test once and the results will be sent to any university that requires your results. 

You will only ever need to take the test once per admissions cycle; for example, if a you are applying to Computer Science at both Imperial and Cambridge, you should take the TMUA in October only. Both universities will be able to use the result in their selection process.

If you are applying to degrees that need different tests (for example, Computer Science at Imperial and Engineering at Cambridge) you will need to take both TMUA and ESAT.