Though the RAC says it's not strictly illegal to undertake - you can be done for careless driving.
Highway code for overtaking
Overtaking (rules 267 to 269)
Rule 267
Do not overtake unless you are sure it is safe and legal to do so. Overtake only on the right. You should
check your mirrors
take time to judge the speeds correctly
make sure that the lane you will be joining is sufficiently clear ahead and behind
take a quick sideways glance into the blind spot area to verify the position of a vehicle that may have disappeared from your view in the mirror
remember that traffic may be coming up behind you very quickly. Check all your mirrors carefully. Look out for motorcyclists. When it is safe to do so, signal in plenty of time, then move out
ensure you do not cut in on the vehicle you have overtaken
be especially careful at night and in poor visibility when it is harder to judge speed and distance.
Rule 268
Do not overtake on the left or move to a lane on your left to overtake. In congested conditions, where adjacent lanes of traffic are moving at similar speeds, traffic in left-hand lanes may sometimes be moving faster than traffic to the right. In these conditions you may keep up with the traffic in your lane even if this means passing traffic in the lane to your right. Do not weave in and out of lanes to overtake.
If you are on the left hand lane already you can keep up with the speed that lane is travelling even if the righthand lanes are travelling slower.
