Offence code TT99 must stay on a driving licence for four years from date of conviction.
Taken from:
http://www.direct.gov.uk/en/Motoring/DriverLicensing/EndorsementsAndDisqualifications/DG_10022425
I wouldn't be so sure of getting more quotes too quickly.
Non disclosure of the full facts is likely to leave you with far more serious problems than you have right now.
CodeOffenceTT99To signify a disqualification under 'totting-up' procedure. If the total of penalty points reaches 12 or more within three years, the driver is liable to be disqualified