Your question is based upon the false assumption that the jury have access to the interview tapes. In practice the Crown Prosecution Service barrister will normally only quote very brief abstracts from the transcripts of the tapes. He/she will take care not to use any abstracts that either refer directly to previous offences or infer that any other offences may have been committed (unless the defendant is also on trial for such alleged offences at the same time).
The defendant (or, more usually, his/her defence team) is always provided with copies of the tapes. The defence barrister could choose to use further abstracts (possibly to show that the CPS evidence was taken out of context) or even to insist that the jury hears all of the tapes (possibly to show that the defendant was put under unreasonable pressure during the interviews). However it's extremely unlikely that this would happen, especially if the interviews referred to previous convictions.
If the defendant (or his defence team) were to refer to his/her previous convictions in court (either directly or by introducing the full interview tapes into evidence) there would be no breach of court procedures and thus no reason for the judge to halt the trial.
As your post suggests, the CPS can't normally make reference to any previous convictions without causing the trial to be abandoned. However, when the defendant's previous convictions indicate a proclivity to commit the type of offence with which he/she is currently charged, the CPS can seek the permission of the court to disclose those previous convictions to the jury. Such applications are often made when a defendant is charged with sexual offences but they're now becoming increasingly common for (alleged) crimes of dishonesty and violence.
Chris