Re: Secret ballot?
"They do write the number of your ballot slip along side of your name in the register, so it is not that secret."
No they don't.
They cross out your name in the publically available marked register. All you can see from ther marked register is that you have been given a ballot paper. Nothing more, and nothing less.
You elector number is written on the counterfoil to the ballot paper. You are given the ballot paper, seperate from the counterfoil. The counterfoil and ballot paper have a serial number on them. The ballots and counterfoild are stored seperately and kept for about a year before being destroyed.
If you have sufficient evidence to convince an electoral court that electoral irregularities may have occured (cf Tower Hemlets), that court may order that the ballots be examined to search for irregularities. If you have sufficient evidence to convince an electoral court that those electoral irregularies are of a sort when a match needs to be made between ballots and electors, then that court may order that election officials take hundreds of hours sorting through tens of thousands of ballot papers to match up the suspicious ballots.
To all intents and purposes, the ballot is secret. Only the voter can breach that secrecy by themselves stating (or ratherm, claiming) who they voted for.