> I've noticed that some trigpoints are tagged with  a reference prefixed
TPUK

I should also have said in my first reply  that the page for each trig on
the trigpointing.uk website gives the source of the OS data that it uses
and shows the OS names.  For example http://trigpointing.uk/trig/4791 describes
what the site calls TP4791.  According to that page the position data is
derived from https://groups.yahoo.com/neo/groups/trigonomy/files/OS%20data/.
The original OS name was TQ47/T218 and the new name is TQ47T218.

So if a trig is referenced on the map using its trigpointing.uk name, you
can look up the OS name via that website.  Since all the pages have the
same form, with a bit of scripting trickery it should be possible to scrape
the conversions from the same website and fix them all in a batch.

The OS uses accurate GPS these days so they don't maintain their trig point
list.  The main purpose of the trigpointing.uk site is to maintain up to
date reports on the state of the trigts - some are destroyed and a few are
still in one piece but not in their original position, due to subsidence.
I think that these data do belong to the site owner, so his permission
would be needed to annotate the map with them.  As I said in my first post,
he may well be willing.
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