Undertaking on motorways

Ok, so I have a question about overtaking/undertaking in the UK. Let’s suppose you’re driving at 70mph on a three lane motorway. You’re on the left lane and see a slow moving vehicle ahead, so in due time you move to the middle lane to pass it and move back to the left lane. That’s a correct overtake to my understanding. But let’s suppose there was a car hogging the right lane at 50mph when you overtook that vehicle on the left lane. Does that mean you’re undertaking that car on the right? Does that mean you need to reduce your speed to 50mph until that driver on the right lane realises he’s wrong and moves to the left otherwise you’re undertaking him?