The actual answer to this is terrible. Courts had to trust the computer was correct. There was a common law presumption that a computer was operating correctly unless there is evidence to the contrary (and getting that evidence is basically impossible for the individuals being charged who were post office workers, not computer experts, and the source code was a trade secret).
This might change, partly in response to this case: https://www.gov.uk/government/calls-for-evidence/use-of-evid...
Quite interesting article about this: https://www.counselmagazine.co.uk/articles/the-presumption-t...