Although the Criminal Records Bureau intend to provide the service at some point, they don't at the moment (they are still trying to get to grips with the checks required of people in high-risk jobs - e.g. teachers, etc.).
You have to apply to the local police force under the Data Protection Act. It will cost you £10. If you are in the Metropolitan Police area (the 32 London Boroughs) you can go to a police station for a form, or download one here.
http://www.met.police.uk/dataprotection/forms.htm
If you send it off you will get a prompt reply saying it will be processed (I know - I asked for a different thing and got one of their standard replies so it seems they are set up for criminal record / PNC checks!!) but the actual result will take longer (they have up to 40 days according to teh rules).
If you are in another police area, check their website for their similar process or call at a police station.
Your conviction, even if it was ever recorded, will be "spent" under the Rehabilitation of Offenders Act 1974 if it is more than five years old (the period is defined by the sentence and a fine = 5 years). So, even if you ever had a proper criminal record, you won't have any more!
http://www.nacro.org.uk/data/resources/nacro-2005020106.pdf
"Spent" convictions always remain on the CRB database and have to be disclosed in high-risk job searches (the "previous convictions" question will always refer to having to disclose all conviction including spent ones if the exemption applie) but otherwise you do not have to disclose them and no-one can make any use of them.