So,

I've forgotten where we started the discussion of this issue but, for those
who are interested, I'll post what I have discovered here

It seems that someone has already asked an FOI that went much of the way to
answering the points I required and the answer (s)he received was:

"this information is already in the public domain, you will find it here"

http://www.londoncouncils.gov.uk/node/23442

That was for 2015-16 as that was when the FOI was raised. Presumably there
are later versions but as I'm only interested in relative not absolute
figures, that will suffice

No doubt someone will pipe up with "but we knew that was there all along" in
which case "why didn't somebody tell me" :-)

And as part of the answer is a link to:

https://www.whatdotheyknow.com/reque..._passthrough=1

which provides addition useful information

Drilling down though the numbers, it seems that the amount charged to each
council is calculated as: the total percentage of the costs of all
concessionary travel made by their residents.

Though when I say concessionary travel, this is just (all flavours) of
Freedom pass. 60+ and National card usage is not detailed in this document.

Quite how the total costs of concessionary travel is calculated is not
clear. The individual total numbers are huge, but when pro rata-ed down to
individual card holders, range from £140.15 for Bexley residents to £405.11
for Hackney. So maybe not so much a big deal.

And whilst I was concerned that boroughs without tube links would be
disproportionally charged by a system that just counted entries/exists for
each mode, and it is also the case that 67% of the costs of all
concessionary travel is for bus travel, it does seem that the final charge
to boroughs that don't have tube line is at the bottom end of the scale -
perhaps those residents simply make fewer/shorter individual journey :-).

Finally, as you can see. It counts rail/tube exits to apportion the change.
How people who make journeys without tapping out are accounted for is
anyone's guess.

And finally,finally. Someone else was fussing about discretionary passes.
You can see from the linked spreadsheet that the number of these passes is
tiny - some boroughs issuing as few as 1 (one) card to their residents, um
resident. I think any non linear effect of these cards on the overall
statistics can be discounted.

tim