1. If an employer doesn't ask about convictions you don't have to disclose them.
2. If an employer asks about convictions, you normally only have to only disclose those which aren't 'spent'. The length of time it takes for a conviction to become spent depends upon the sentence which was imposed for the offence. See here for details:
http://www.lawontheweb.co.uk/rehabact.htm
Failure to disclose an unspent conviction, when required to do so, could render any contract of employment invalid. (i.e. the employer could sack the employee if the offence later came to the attention of the employer). It could also lead to a further criminal conviction for 'seeking to obtain a pecuniary advantage by deception').
3. Some types of employment are exempted from the provisions of the Rehabilitation of Offenders Act. (This relates mainly to employment involved in the administration of justice -e.g. police, prison service, etc - or working alongside children or vulnerable adults - e.g. teaching, school caretaker, nursing, hospital porter, etc). When applying for these types of employment, convictions are never regarded as spent and must always be declared.
4. For certain types of employment (primarily those referred to in paragraph 3) employers can seek a check with the Criminal Records Bureau. Any CRB check will always show all convictions, including those which would normally be regarded as spent.
The foregoing paragraphs relate to all criminal offences, including those under the Public Order Act.
Chris