On the Singers, there are both straight pins and modified Simplex seatposts. The Simplex is easy to modify, because it has a closed top, with the clamp being on the sides. A hole for a bolt, maybe some reinforcement, and a wedge at the bottom.
On the older Singer bikes with internal expander, the post diameter usually is 25.0 mm, just as Brian Baylis surmised.
There were numerous other seatposts with internal clamps. I have one which featured a 2-bolt clamp similar to a Campy NR, but accessible from the bottom. Neat design.
Jan Heine, Seattle
Vintage Bicycle Quarterly