FWIW I find a Plain type seat post and the Brompton Penta clip works perfectly..
[Wall Bike even cherry picks them to sell, thru their store, though they dont sell the Bikes ]

I use the old 2 bolt Campag seat post with my Brooks Pro. Campag's wrench [771] for the bolt heads on top
has an open end wrench that fits the Brooks tension nut.
Tullio, one would presume, designed the seat post for Brooks saddles ..