Hi
What year is the Carlton and which model? on reflection my guess would be 5/32" which would be the slightly smaller ones. I guess you don't have the originals to compare.
Take the smaller ones and fill the screw race for the forks (holding with grease) full of balls, take one out and seat it on the top of the frame (race in head tube) just by hand. It should fit nicely with none of the parts of the headset touching.....
Shaun