So, I've managed to find a workable solution.
1. Plan route in cycle.travel
2. Download route for GPS selecting the option" GPX route (small file, marks turns)"
3. Load file into Brouter via "load track as route" option (uncheck "load waypoints as POIs")
4. Check route in Brouter has been plotted correctly
5. In Brouter set turn instruction mode to "orux-style"
6. Export route from Brouter (uncheck include waypoints"
7. Load route into Oruxmaps and ride!