I have had a similar idea to this for a long time, so I'm delighted to see it proposed here. Clearly there could be dangers where individuals fall across two 'tracks' but hopefully in such cases they would be 'swept' onto the slower track by the faster moving one.
Certainly it would be healthier, faster and quicker and it could also be much more pleasant if the tunnels were made attractive. What a boon in bad weather!
Perhaps more such travelator routes would follow and we'd all be better off for the reduced congestion, waiting and cramming into overcrowded trains.
Good luck to NBBJ. I hope to see it happen!

OMG, most people don't even know how to use the basic escalator keep to the right except to pass....this could get ugly one person falls sideways and the opposite lane?

there is a long history from the 70's of people experimenting with as well as proposing long distance moving walk ways.
there is no question they 'could' theoretically be more efficient. the reality in MANY experiments is simply that they are not.
this reality is from practical experience of building a few. read your history in this area it is worth it.
the underlying solution is that you cannot move large objects continuously running them. escalators are not even that big and they tend to have all sorts of maintanance problems. there are probably many problems this is the case, but the likely primary candidate is that all sorts of traction and friction cause vibration of all types that reverberates and causes more damage the larger the thing being moved.
the solution is obvious magnetically levitated small platforms that move slowly, as modular items, even one behind the other (nearly continous), on a long track rather than continuous piece of large walkway.
this way, the gaps between the modular units don't transmit vibration and if one platform breaks just replace it modular, you don't need to stop and fix the whole thing.
pretty obvious solution, but that's only because over 2 decades of experiments actually yielded WISDOM from engineering. if you cannot learn from other's hard earned mistakes/troubles/obstacles, you cannot make progress.

Another thing they appear to have forgotten - the train moves the air in the tunnel this system would not, therefore there would be a need for some very large fans to circulate the air and keep it fresh.
Another thing, you need travel in two directions - no one is going to travel all the way round just to get to a station a few stops before their station.
Also, how would this cope with the massive influx of people at rush hour?

"The roads must roll"

I'm not familiar with London's underground system but in Melbourne we have an up and a down line in separate tunnels. If that is the case in London that would obviously alleviate some of problems indicated by other comments here. Comments about the freshness off the air also seem a little under thought. Trains are relatively enclosed systems but tunnels are not. Chimneys would draw air through the system passively and only work better with the greater body heat of greater numbers.

Underground schweeb or hyperloop pods please. The engineering/maintenance would be horrendous. Good for creating jobs though.

There goes my nap.

If you've ever seen the mass of bodies waiting to board a train, and then imagine multiple masses from multiple platforms all piling on at once, at rush hour, and all jumping onto the 'fast lane' the load would be enormous. [Imagine a football stadium of people all boarding at once.] Failures would be a nightmare, as the whole local system for that 'station' would have to be shut down in order for repairs to be made.

If this can be made to work out, and the history does suggest a bunch of significant "IFs", then the first and second stations should be named for Arthur C.Clarke and Isaac Asimov. Good Luck with this!