Roof extensions always require planning permission within a Conservation Area as Class B domestic permitted development rights do not apply. You should however be able to install roof-lights within the front and rear roof-slopes of the house to facilitate the use of existing loft space as long as those roof-lights are flush with the roof-slope, as that would be permitted development under Class C.If you were intending to pursue a planning application, you would be wise to read both LB Hounslow's Residential Extension Guidelines (which can be found at the following link - https://www.hounslow.gov.uk/info/20035/planning_permission/1479/residential_extension_guidelinesand it would also be wise to read the Turnham Green Conservation Area Appraisal (which for some reason isn't downloading to my PC at the moment). As Vanessa says you would also be wise to contact the Conservation Officer, although getting hold of an Officer by phone to discuss a speculative domestic extension proposal could be difficult.
Adam Beamish ● 1715d