A really secret ballot, Ebbie. The voter's entitlement to vote, at the polling station authorised by his residence and no other, must be carefully checked by the production of his voter's papers and ID. He must then be crossed or ticked off on the list so that he cannot come and try to vote again; then issued with a plain, unnumbered ballot paper [or if numbered for admin purposes, in no way linked in writing to him, by counterfoil or any other method]. He will then cast his vote in a private booth and put his folded paper into the ballot box.

If the vote is to be truly secret, there must be no possible or potential method of linking the ballot paper with the voter.

At present there is. It is not easy, or untroublesome ~~ but it could be done. So long as that is the case, the claim of a 'secret ballot' is unsustainable.

But the system you suggest only omits the step of numbering the ballots.
If we are going down the 'secret police' scenario then you need to ensure that voters don't leave their fingerprints on the ballots as well!

The current system works, and is about as 'secret' as we're liable to get.