How to insulate behind cladding on old barn?

[The barn]

I want to improve the insulation of my old barn.  I have underfloor heating but the external walls let out all the heat.  It has featherboard cladding on the outside which has shrunk so there are gaps on the sides in lots of places.  Behind the featherboard is about 50cm of celotex and some black membrane in places then plasterboard.  From the inside, you can also feel the cold air in the holes in the wooden beams.  What is the best way to improve it?  My builders says I should remove the existing featherboard, batten and then put some sort of insulation material and then put new featherboard back on.  The council will only let me use wood as I am in a conservation area.   Any suggestions for the best type of insulation?  I would prefer not to do any work on the inside if possible but that may be the best way to do it.   

[George]

Remove the cladding, seal any gaps in the existing celotex and tape the joints. Then overlay with more PIR insulation boards, tape the joints and cover with a breather membrane.

 

50mm battens and then reuse the timbers (but replace anything rotten or badly warped).

 

An extra 50mm of PIR will help, but you need to have a look at the eaves and make sure that will still work. If you go for 100mm you'll be toasty.