OSM default for what it classes as "trunk" roads (which is different from UK definition) is "unknown".

I removed the cycleway because there is no cycleway.

But the previous tagging - bicycle=no - was wrong and needed correcting.

Also checking the route of the cycle path navigating the A683 Eastwards (Morcambe-> Caton). After stopping for TWELVE separate signal crossings you are dumped on the slip road for the Motorway - so not a viable route in any case. I have added cycling=yes to that stretch of slip road so at least the route is available for west bound cyclists with plenty of time on their hands.

Unfortunately, while the "default" is for cyclists to be able to use the roads, there are a growing number of roads where cycling is being prohibited, so it is necessary to tag main roads to keep track of this.

Fortunately, in the UK there is no obligation to ride on the pavement just because it has been designated for use by bicycles - in the same way motorists are still allowed to drive on the A6 even though there is a parallel motorway explicitly mapped for motors..

I think it must have been this one:
https://goo.gl/maps/FUpd6Q5WafT2
Note the sign with a cycle surrounded by a red circle - this means NO CYCLING. You would be better trying to persuade the council to allow it rather than get cyclestreets to recommend illegal routes.

Which particular path are you refering to?

Whatever a "motorroad" is cycling is permitted on this stretch of the oxford bypass - so it can't be one. Cycling is prohibited on part of the eastern bypass.

Changed back - but the designation is historic. These roads do not form part of Warrington's primary network anymore and are not signed on the ground.