You can complain but those are very different processes: at this time, it’s your neighbor’s responsibility to obtain your approval, the burden is on them to come to a solution. If you see that there is a problem afterwards, it’s on you to fill a complaint, then see that it is processed.
All the stories about complaints I have heard point to emotional stress and scars staying during and often after the process. It’s very worth it to do things properly beforehand to keep that very valuable good relationship you have with your neighbors (congrats!).
If you reach an agreement that doesn’t get everything settled at once, it adds enough value to your house to make it worth the fees and it wouldn’t taint the good relationship you have with your neighbors, I’d say it’s worth it to have it written on the land registry: one scenario that could occur is that your neighbors sell their house, in which case, most agreements you had with them would be void (but anything written on the land registry would still stand).
I don’t know the proper situation but 20cm doesn’t seem a huge deal to me. I’d probably be more annoyed by the fact that they had to be forced to get my agreement to come and see me to talk about it than by the new elevation itself.