Depends on the record. The Rehabilitation of Offenders Act lays out if/when a conviction will be 'spent' so you don't have to declare it to employers etc. The rules depend on what you did and the age you were when you did it.
As for police records, check out the FAQs of the Criminal Records Bureau site.
http://www.crb.gov.uk/index.asp
The Police National Computer (PNC) only holds details of �Recordable� offences e.g. those offences for which a prison sentence could be given so most driving offences are not on the PNC.
To comply with the Data Protection Act, the Association of Chief Police Officers (ACPO) have set out guidelines for police forces to remove certain offences that took place more than 10 years ago and the person has not been convicted of another offence since that time. The same applies to cautions but the period used is 5 years. There are some exceptions to these guidelines.
three or more convictions for recordable offences - the record will be kept for 20 years
a custodial sentence, including suspended sentences, amounting to six months or more - the record will be kept for life
been convicted of indecency; sexual offences; violence offences; possession of class A drugs; or trafficking in, importation of, or supply of any drug, - the record is kept for life
been found unfit to plead for reason of insanity, or has been sentenced under the Mental Health Act - record kept for life
been convicted of an offence involving a child or vulnerable adult where their modus operandi indicates that the person deliberately targets such people, in which case the record will be kept for life.