A criminal record is for life.
A conditional discharge becomes 'spent' (for most purposes) after one year or at the end of the period for which it applies (whichever is the longer). That means that for most purposes (e.g. insurance applications and most job applications) you won't need to declare your conviction after that time.
However, some types of employment are exempt from the provisions of the Rehabilitation of Offenders Act. These include jobs involved in the administration of justice and working with, or alongside, children or vulnerable adults. When applying for these jobs, you'll always have to declare your conviction and, if the employer carries out a check with the Criminal Records Bureau, your conviction will always show up.
An employer can only dismiss someone from employment, for a criminal offence committed outside of that employment, when it can be shown that it is inappropriate for the employee to remain in that post.
If a teacher was convicted of failing to ensure that their own child attended school, the governors of the school would have to ask themselves whether, based upon the inevitable bad publicity, parents would lose faith in the ability of the teacher.
Similarly, if the employee worked as a lunch-time supervisor, the governors might take the view that parents could take the attitude "If she can't control her own daughter, what right has she to be in charge of our kids?". (They might, thus, decide that it's inappropriate for the employee to remain in post, based upon a 'loss of trust').
However, if the employee worked in the school kitchens, and had little contact with pupils, it's unlikely that there would be grounds for dismissal.
Chris