There is a difference between committing a traffic offence and being criminally convicted in a court. I think I know the home office enough by now and know exactly what they look for to refuse one's application. If they start refusing applications based on minor traffic offences and assuming that 90% of all applicants have driven in the U.K for at least a year or two, one can do a simple calculation of the percentage of refusals in a year which is simply not the case. As far as Fayed is concerned, only if all the applicants are all rich and famous like him and not forgetting ''controversial'', I won't be surprised if they keep rejecting their applications.
Rest assured, nothing to be afraid of if you have ''minor'' traffic offences!!!