As Eddie has stated, when magistrates (or a judge) consider sentencing they will always be made aware of any previous convictions against the offender.
It occurs to me though that your question might relate to an earlier stage in the court proceedings, i.e. during a trial. The normal rule is that no evidence relating to previous offences can be put before a court during a trial. However, under certain circumstances, the prosecution can apply for 'evidence of bad character' to be put before a court if it may show that the defendant has a 'propensity' for committing certain types of crime.
A 'bad character' application is most often made in cases relating to sexual offences. (e.g. someone who was charged with downloading child porn might claim that someone else had downloaded the images onto their computer, but the prosecution could seek permission to tell the court that the defendant had several previous convictions for similar offences, making his defence seem less credible). However 'bad character' applications are increasingly being sought, and granted, in other types of case.
Given the circumstances you describe, it's unlikely that the CPS would make a 'bad character' application unless there was clearly some type of link between the first offence and the current (alleged) offence.
Chris