I am replying to some of the questions asked by Graham Whaley. For less expert 
readers, I have tried to explain some of the technical terms, at the end of 
this message.

There are a couple of slips in what Chris Andrew wrote. The difference between 
ODN and EGM96 is less than a metre. And (in the UK) EGM96 is above the 
ellipsoid.

For ele tags, I would specify four:
ele
ele:EGM96
ele:ODN
ele:WGS84
The ele tag would contain the EGM96 value. This is my way of complying with the 
recommendation that the the ele tag should be referred to EGM96, while making 
it crystal clear what is going on. I am assuming that man_made=survey_point 
would not generally be rendered in maps, so that the presence of decimals in 
ele values would not be a problem. If someone produced a specialist map showing 
survey points, they could choose how to deal with the decimals, e.g. they could 
round the values if the decimals are cluttering the map.

This is an example of my tagging of a peak: 
https://www.openstreetmap.org/node/518577471

The ele:ODN value could be as given by the Ordnance Survey, with however many 
decimals there were. I prefer ele:ODN to ele:local because it is clearer what 
the reference is. I would retain all the decimal places in the calculations, 
but then round the other ele values to the nearest centimetre (2 decimal 
places) because the third decimal place (millimetres) would not be meaningful. 
I say this, because of this quote "The National Geoid Model OSGM15 is a grid of 
geoid-ellipsoid separation values... The nominal accuracy of the geoid model is 
8 mm rms (root mean square) in mainland UK..." which comes from here 
https://docs.os.uk/more-than-maps/a-guide-to-coordinate-systems-in-great-britain/from-one-coordinate-system-to-another-geodetic-transformations/national-geoid-model-osgm15-etrs89-orthometric-height
 (very long URL).

Now, the conversion to latitude, longitude and EGM96 height. As examples, I 
have chosen two triangulation pillars more or less at random, one, well to the 
south and one, well to the north.
Box Hill trig point https://www.openstreetmap.org/node/4267733568
Strathy Point trig point https://www.openstreetmap.org/node/612893275
British National Grid (BNG) eastings and northings from OS:
Box Hill 517971.06 151163.16
Strathy Point 282007.756 968512.562
Box Hill height is 171.968 in trig archive and 171.9682 in benchmark archive.
Strathy Point height is 90.293 in trig archive and 90.294 in benchmark archive.

I did a manual conversion giving these results (these really need to be 
displayed with a monospaced font as in the mailing list web pages):
Ht of EGM96 Ht above Offset from
ODN HAE geoid EGM96 geoid Latitude Longitude OSM object
Box Hill 171.968 217.439 45.809 171.630 51.2474475 -0.3111227 0.82m
Strathy Point 90.293 143.410 53.686 89.724 58.5885068 -4.0314345 13.00m
You can see that the difference between ele:ODN and ele:EGM96 is 30-60cm. The 
height of the geoid is within the range given by Chris Andrew. You can use 
these results to check your calculations. You will sometimes see a difference 
of 1 in the 7th decimal place of latitude and longitude. I suggest you 
replicate my manual conversions (to give confidence in the process) and then do 
a couple more trig points in the same way, to give a more comprehensive check 
on your calculations. How I did it...

I downloaded the Ordnance Survey Grid InQuestII application from 
https://www.ordnancesurvey.co.uk/geodesy-positioning/coordinate-transformations/grid-inquest2-software
 . You need to set suitable numbers of decimal places for the input and output 
boxes, in the options. Then I did a conversion from OSGB36/BNG to ETRS89 
geodetic. This gave me the latitude, the longitude and the height above the 
ellipsoid (HAE, the ele:WGS84 value). Then I obtained the height of the EGM96 
geoid (above the ellipsoid) from 
https://geographiclib.sourceforge.io/cgi-bin/GeoidEval . Then the height 
relative to the EGM96 geoid is a simple subtraction. Then the last stage is 
optional... In JOSM, I created a node at the position of the trig point. I drew 
a way from there to the OSM object. With the way selected, the status bar gives 
its length, i.e. the offset. (If you only see one decimal place, you need to 
change statusbar.decimal-format to 0.00 in the expert preferences and restart.)

You can see that I have guided you to ETRS89 coordinates. This is because, in 
Great Britain, we are recommending that users align aerial imagery to the OSMUK 
Cadastral Parcels before tracing features. The Cadastral Parcels are based on 
Ordnance Survey data which is aligned to ETRS89. ETRS89 can be regarded as 
WGS84 epoch 1989.0, in other words, the WGS84 coordinates as they were at the 
beginning of 1989. WGS84 coordinates in Europe move at 25mm per year relative 
to the land because of the motion of the Eurasian tectonic plate. So the 
difference between epochs 1989.0 and 2026.0 is a little over 90cm. In contrast, 
the Cadastral Parcels do not move relative to the land. They remain at the 
property boundaries. They track the tectonic plate - ETRS89 is a plate-fixed 
datum.

Finally, an explanation of some technical terms.

The geoid is the shape of the earth - of a level surface at sea level. It is 
uneven because of variations in density from place to place within the earth. 
It is usually expressed in terms of the height relative to the ellipsoid.

"The ellipsoid" is the GRS80 ellipsoid, used by WGS84 and ETRS89. An ellipsoid 
is a geometrical figure, a "squashed sphere". Because it is a geometrical 
figure, we can work with it, using equations. The ellipsoid provides a rough 
approximation to the shape of the earth. A GNSS receiver measures the height 
above the ellipsoid - HAE is the raw data. GNSS stands for Global Navigation 
Satellite System. Many GNSS receivers contain a geoid model so that they can do 
an approximate conversion to height above sea level.

A geoid model - such as EGM96 - provides a much closer approximation to the 
shape of the earth. It is essentially a set of numbers which describe the 
details of the shape. EGM stands for Earth Gravitational Model.

ODN is the Ordnance Datum Newlyn. It is the Ordnance Survey's geoid model, 
covering Great Britain. It is the zero altitude reference level ("sea level") 
for all heights given by the Ordnance Survey.

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