It is a civil offence, not a criminal.
Driving without insurance is a criminal offence - albeit a traffic offence. It is by no means 'civil'. Hence why such cases are tried in criminal courts, when circumstances dictate.
The power to record offences (as in Criminal Records) is defined by the National Police Records (Recordable Offences) Regulations 2000. There are also certain convictions which become 'spent' under terms of the Rehabilitation of Offenders Act 1974, so that even older, more serious convictions won't show up.
As far as I'm aware, driving without insurance (S143 of the Road Traffic Act 1988) is not a recordable offence, and will not show up on PNC, and any subsequent CRB check or Disclosure check. Unless of course, the OP was charged at the same time with a recordable offence (any offence punishable by imprisonment, or as stated in the schedule of the above regulations), in which both offences would be recorded.
Personally, I don't think you've much to worry about, but if you wish to be sure for your own peace of mind, most Police forces will have a 'subject access' form which you can submit to your local force, and they will return any details of offences that are recorded on PNC about you. If resident in Scotland, this will show CHS check results as well. There is usually a small charge for this, about £10, and it can take a few weeks.
The points on your licence will stop 'totting up' after three years, and you can apply to have them removed after four.
For informations sake - you can see which common traffic offences are 'punishable by imprisonment' (and thus, recorded offences) using this table here:
Penalties : Directgov - Travel and transport
Hope that helps.