An additional house or knock down and build one new house?
If the latter (which i think is what you mean) then you are always allowed to build something of the same volume as you knock down, but the local authority will need to agree the design. There is no guarantee they will let you do anything other than rebuild brick for brick what is already there, especially if in a conservation area, but so long as what you what is sympathetic to the character of the area, doesn't rob the neighbours of light or privacy and isn't loads bigger than what you squash you can usually get something interesting agreed.
An additional house or knock down and build one new house?
If the latter (which i think is what you mean) then you are always allowed to build something of the same volume as you knock down, but the local authority will need to agree the design. There is no guarantee they will let you do anything other than rebuild brick for brick what is already there, especially if in a conservation area, but so long as what you what is sympathetic to the character of the area, doesn't rob the neighbours of light or privacy and isn't loads bigger than what you squash you can usually get something interesting agreed.