As a consequence these are the about heights of the different stems (not bars):
M (before 2018): 31,5 cm
P: 31,5 cm
M (after 2018): 34,5 cm
S: 37,5 cm
H (before 2018): 37,5 cm
H after 2018: 40,5 cm
For the T-line the world is different again: There are only a M and a S model available - however: Both are using the same stem. So only one type of stem avail. on the T-Line. Did not measure it's height until now as I forgot to do it when I had one in my hands a while ago.
Stem height. Not bar height.
Despite
@T4tomo obviously not haven got the topic it is easy to fulfil your desire:
The S-stem is 37,5 cm and this results (with straight S-bars) in 925mm bar height. Which teaches us that to each stem we have to add 925mm-375mm=550mm = 55cm to get the overall height of a given stem on the Brompton.
M (before 2018): 31,5 cm -> 86,5cm
P: 31,5 cm -> 86,5cm
M (after 2018): 34,5 cm -> 89,5cm
S: 37,5 cm -> 92,5cm
H (before 2018): 37,5 cm -> 92,5cm
H after 2018: 40,5 cm -> 95,5 cm
However, the height from the ground will differ slightly depending from which tyres you mount. It is not a too helpful measurement also as you rather want to know the difference between pedal height and bar height if you want to do a bikefit and this depends from the height of the bottom bracket and the length of the cranks...
The whole point is that I've never seen anything that on Google or elsewhere that shows the stem heights. Given that the OP was trying to determine what would happen if you put flat bars on an M stem it would be useful information.
If it did exist on Google (in an easily digestible form), I'd imagine that someone would have linked to it in one of the many, many threads about bar heights and bar swaps.
Indeed this information as to my knowledge does not exist. We tried to collect it for quite a while in the former Bromptonauten forum and once we were more or less done Brompton introduced the new stems
But now you have it at your convenience, H-stems (old and new) measured by your's truly today and derivated the other values from there based on historical knowledge about their relations.