The relevant legislation is the Rehabilitation of Offenders Act 1974 in conjunction with the Road Traffic Offenders Act 1988. However the situation you describe is inaccurate for disqualification (it accurately describes endorsement).
The rehabilitation period for a disqualification is the length of the disqualification. If a person is disqualified at the same time as receiving another penalty, the longer rehabilitation period applies. E.g. if a motorist is banned from driving for seven years and fined - which ordinarily takes five years to become spent - the rehabilitation period would be seven years, not five years.
An endorsement is not a 'disability, prohibition or other penalty' within the meaning of ROA 1974, and therefore it cannot affect the rehabilitation period of a motoring conviction. So, for example, if a motorist is fined for drink driving and has his or her licence endorsed, the rehabilitation period would be five years (the length applicable to the fine) rather than 11 years (the length of time before a driver convicted of drink driving is entitled to a clean driving licence).