You are continuing to ignore some rather fundamental factors that affect modal choice, in particular travel distances. London is bigger than Copenhagen and Amsterdam. Commuting distances are greater. Buses are used for longer distance trips than cycling. You can't have 40% modal share for cycling unless 40% of trips are within reasonable cycling distance, i.e. cycling is comparable in journey time. So, to go alongside dellzeqq's "show us the drawing" challenge, here's another one for you: "show us the trips".
EH? Since when is it assumed that everything a local authority does is the rational thing, or the most cost-effective thing? Why do I have to justify measures I don't think are necessary? There are plenty of reasons why ineffective cycling infrastructure is installed, and one of those is that people like you keep demanding it!
In any case, I didn't say that all the cycling infrastructure installed in Oxford or Cambridge is pointless. Some of it is beneficial, but you've still missed the fundamental point, which is that the main growth in cycling took place before it, demonstrating that separate provision is not a necessary condition for getting more people to cycle. Once you've grasped the significance of that then you'll start to understand that modal choice is rather more complex than you think it is.