Loft conversion - appeal for planning permission to slightly raise roof ridge line

[peonylover22]

Me and my loft conversion again.
We lack 20cm of the required height for a loft conversion. Ideally we would

Ooops.
Ideally we would like to raise the roof ridge line by 20cm, but our local authority do not grant planning permission for roof raises, however slight.
Has anyone successfully appealed against a local authority refusal to grant planning permission to raise the roof ridge?
The property is an Edwardian terraced house (end of terrace). It is not a conservation area. The reason given by the council is that they set importance in a uniform roofline, but the roofline is not uniform on the road as we are on the top of a hill, so the roofs step up in height every couple of houses. There are also a number of illicit upward loft conversions where the council has not sought to enforce the breach in planning.
Any thoughts?

Why can't you lower the ceilings in the rooms below?

We have done two loft conversions now in two Victorian properties and always had room.

Not for raising the roof but we are in a conservation zone and had our planning permission for a loft conversion turned down. We appealed and won.