Lets do some numbers to work out how thick the insulation needs to be to give roughly the same level of insulation as the wall of a new house...
The web site for the cabin says the walls have a U-Value of 1.9 W/m^2K.
I believe a new house typically has walls with a U-Value of around 0.27 to 0.3 W/m^2K. Lets call it 0.27.
First convert both of the above to Thermal Resistance = 1/U-Value...
Cabin walls have a thermal resistance of 1/1.9 = 0.53
New house wall thermal resistance is 1/0.27 = 3.7
That means the insulation and plasterboard must add 3.7 - 0.53 = 3.17
I think plasterboard has a thermal resistance of about 0.06 meaning the insulation must provide 3.17 - 0.06 = 3.11
Celotex/Kingspan type foams have a thermal resistance per meter thickness of about 43 so you need around..
3.11/43 x 1000 = 72mm
So something like 70mm Celotex GA3000 or Kingspan K8 would seem to be ideal. You could fit less and the results would be roughly in proportion to thickness. (eg half as thick would be roughly half as good). Upto you really.
If that's too expensive I would look at
http://www.secondsandco.co.uk/ to see if they have anything close.