I want to add a single-storey side extension with a flat roof. We live in a conservation area. Am I limited to 50% of original width?

The 50% rule is only applicable to buildings that comply with Permitted Development (PD) rights. As PD rights do not extend to a conservation area, you will need to submit a full householder planning application. However, flat roofs may be refused in a conservation area. I suggest that you search the planning portal in your area and see what has been allowed and what objections have been raised. By walking around your area, you will get an idea of what materials are acceptable.