Fast Lanes Are a No
As you correctly point out, the UK is one of those countries where vehicles drive on the left hand lane. This means that overtaking is done by passing vehicles on the right. I don't think that a the concept of a fast lane exists on UK motorways since one should always occupy the leftmost free lane and switch to adjacent lanes on the right solely to overtake. Indeed this is reflected the UK Highway Code:
You should always drive in the left-hand lane when the road ahead is clear. If you are overtaking a number of slower-moving vehicles, you should return to the left-hand lane as soon as you are safely past.
So Is Undertaking
For completeness sake note that undertaking, I.e. passing vehicles on their inside (left) lane is forbidden in the UK, except for when dense traffic conditions force vehicle to proceed slowly on parallel lanes. Quoting from the UK Highway Code:
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.