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On the whole it is not permissible, in a criminal case, to attempt to prejudice the court against the accused by producing Evidence of unrelated prior criminal activities. If the accused is found guilty, then such information may be relevant to sentencing, but it is not probative in a particular case.
However, where the previous history of the accused does have the direct effect of showing that it is more likely that he commited the offence by tried, this may be permissible. Evidence of this meta is usually called 'similar facts' evidence.
For example, if the accused denies committing the offence at all, and it can be shown that the offence is extremely similar to a prior offence for which he was convicted, this may be admissible (see: Admissibility Of Evidence). If the similar facts are the only evidence that the prosecution has, then the previous conviction must be in a manner that is a 'hallmark' of the accused, and exceptionally unlikely to be commited by anyone else.
The law of 'similar fact evidence' is a development of the courts, and all the associated caselaw will become somewhat irrelevant when the CJA_2003 comes into force. See evidence in chief of bad character for discussion.