Hardly "heavy traffic", the side tunnels are shared between cycles and cars/taxis. Anything that's much bigger won't fit.
Well this looks like the first UK example I've seen of what our Dutch friends call a "fietsstraat" or bike street. The concept is quite well used there, but the circumstances are quite different.
In both cases, the bike lane goes down the centre, and cars are not allowed to overtake bikes, but that's where the similarities end.
In the Dutch cases, the street might typically have a VERY high number of bikes on it - even by Dutch standards, as it might form part of a through route for bikes, but it is only used by cars to access properties on that street.
So let's say, for example, there was a north-south cycle route instead of the foot path which runs along the River Crane, and it then connected towards Bath Road via Waye Ave. If this formed part of a busy cycle route (fat chance at the moment, but say this was just to the east of Schiphol) - you might get as much as 90% of traffic on that road being bicycles, as there's no through road traffic.
So some bright spark has taken this concept and said - let's change a traffic free route and allow cars on it. Except that these cars want to get to an airport. Fast. I've only glanced a few comments in cycle forums and views seem to be mixed - some say the cars / taxis "behave", others say it is very intimidating.
If I was a driver with a flight to catch and the main tunnels were moving like treacle, then I'd see the "left" tunnel as a bit of a gamble. We used to have a level crossing like this - cut through and it will save you 3 minutes, but every now and then you'd get fast then local westbound and local then fast east, with the station being just to the west of the crossing, and that combo could cost you 25 minutes.
Either way - non-motorised access to Heathrow is a dog's breakfast.
That link seems to have vanished too.