It is not about what section of the Road Traffic Act to refer to, more about what is not there if that makes sense.
The specific offence of nearside overtake (undertaking) was removed from the statute with the introduction of the 1972 Road Traffic Act.
To this end, everything came under and was covered either by section 2, which at that time was reckless driving but has now been changed to dangerous, or the section 3 offence which is driving without due care and attention or without reasonable consideration to other road users.
To prove either of these 2 offences, it has to be shown that the standard of driving/riding fell well below that expected of a reasonably competent driver, and the simple act of nearside overtake does not in itself prove the offence.
The reason why is because of the number of times vehicles were stationary in say lane 3 of a motorway due to queuing traffic whilst lanes 1 and 2 remained empty because people belived that they could not pass along the nearside.
Lane discipline also had a bearing. So many people hog the centre lane when lane 1 was clear, it was considered inappropriate to report the person driving down the nearside, when it was the driver in the centre lane in affect reducing the carriageway to a two instead of a three lane road, and the list goes on.
Where people do come unstuck is when they start weaving from lane to lane. For example I was on the M4 on Monday when I saw a bike undertake in lane 1, shoot across to lane 3 and then back into lane 2 before reverting to lane 1 and then back into lane 2 passing vehicles all the time but all in the space of about a quarter to half a mile.
There have been a few cases won recently by injured riders where the defence has used the undertaking action as their principle defence only to lose out because they did not understand or more to the point, were not aware of the legalities.
But back to your original point, there is no specific offence of nearside overtake, the prosecution would have to prove a dangerous or careless driving, and the act of undertaking is not on its own sufficient to secure a conviction.