DVLA is more concerned with vehicle licensing. It used to be Driving Standard Agency (DSA), now the name changed, I am sure for what. They have all the data for all driving centres, but there are issues with data protection, as far as I remember they cannot provide the names of the candidates. But it does take time for the answer, it was waiting more than month.
The Department for Transport in the UK keeps a LOT of statistics. You may find what you need on this page https://www.gov.uk/government/statistical-data-sets/drt02-practical-car-test-pass-rates