Since the existing fascia is sound, that would be fine, Gnessie..........
But ................. the inch under the overhang allows rainwater to drip away safely without touching the fascia. If you reduce this overhang to almost nothing, then rain will constantly run down the face and discolour the paint... and eventually rot the timber.
This would be a better option... only 10mm thick, and no painting!
http://www.nationalplastics.co.uk/fascias-soffits/fascia-board.html
I know that not everyone likes uPVC, but, if you don't like the colours, then it can be painted.