... no, sorry, that is not right. He/she writes your electoral roll number on the ballot paper's numbered counterfoil. It would be an arduous task to correlate all these numbers, and I am sure that all the safeguards and procedures rubricated in the regulations copied above by Nigel are strictly adhered to.
But the fact of the matter remains that the ballot paper & the voter who completed it COULD be correlated; which makes claims of absolute secrecy invalid. "Secret" is not a relative. Nothing can be 'a bit unique'; and, by the same token, nothing can be 'a bit secret'. "Secret" is an absolute; in the context of elections, it means that no-one should be able by any possible means to correlate a voting paper with a specific voter. Once that can be done, it ceases to be "secret", and becomes "sort of secret so long as everyone is correctly motivated and all the rules are observed":