If you've got an uninsulated cavity, even better. Don't even consider
failing to insulate the cavity whilst you're having the work done. The
final resulting building will probably require less than half the heating
of the previous poorly insulated house.

Half?

The whole existing loft would need thicker insulation. Insulating a
cavity
in what is now an internal wall. will help, not a great deal.

Perhaps I didn't make myself clear. I meant cavity insulating the entire
original house, not just the dividing wall.

Christian.