Based on what I've seen from the Libre, I find it very variable across different injections as to the delay on Novorapid.
Under normal circumstances, injecting subcutaneously, it can take, for me, between 30 mins and 1 hour to have an effect. Intramuscular, it's about ten minutes.
This can vary dependent on a number of factors though, including the amount of exercise I've done the previous day, which I've seen push insulin resistance up dramatically.
Are you sure your Levemir levels are correct? Basal requirements do change, and that can affect the way that fast acting insulins work. That can often be an issue in this kind of situation. It's worth using a basal test to ensure that it is not linked to that.
Also, how are you using Levemir? Is it being delivered once or twice daily? The new NICE guidelines state that the best control with Levemir is obtained through twice daily injections.