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they have a mechanism to go back to you
That doesnt sound very anonymous.
It's definitely anonymous once the time limit has passed and no-one has called the vote fraudulent.
The hand written list that ties your electoral roll number with the unique ballot paper ID is sealed up after the polls close.
If there's a question of voter fraud then it gets reopened and the votes can be inspected to see if someone voted more than once/etc. Once the question of fraud has been addressed then the ballot papers and the cross reference lists get incinerated.
If there's no question of voter fraud then, at some point after the election/referendum, the ballot papers and sealed cross reference lists are incinerated.
There should never be a permanent record of how individuals cast their votes.
It is anonymous but in the case of foul-play they have a mechanism to go back to you and say "hey sausagefingers did you vote x"