Noddyholder
Planning often does seem mad, but if the Council has placed an article 4 (I think) direction on your conservation area, then it would mean (for example) that planning permission is required for any material change to the appearance of windows or doors. Obviously, this is meant to stop people taking out nice doors and putting in, say, UPVC. But unfortunately, it also has the effect of requiring planning permission to take out something inappropriate and putting something nicer back in place.
The Council and the Planners are only interpreting the legislation that the Government wrote! It often doesn't make sense to Planners either, but it doesn't really help you if the Planners say 'this is really stupid and I don't think you should have to do it but you need planning permission, with fully detailed drawings'.
You could double check with the Council what the article 4 direction says in case it doesn't deal with back doors?
But if the Council found out you've done the work, they could take enforcement action to make you put it right (obviously highly unlikely in these circumstances - make sure you get a picture of the door at it's most ugly!)
And I'd second what others say about consequences on resale - bit of an unknown quantity as it depends at the moment on how good the purchasers solicitors are, but if the 'home information packs' (not sure what their real name is) you will have to declare 'I've not done anything to the house that needed planning permission' or 'here is the planning permission for what I've done'.