The answer seems to be adjudications.
From one of Tim Harding's articles at http://www.chesscafe.com/text/kibitz123.pdf,
we find
The First Oxford-Cambridge University
Match
On Friday 28 March, 1873, the City of London Chess Club played host for
the chess event that attracted the largest crowd of spectators hitherto known
for any chess contest.
and also
There's also an illustration of play in progress - no clocks visible.Steinitz now takes up the story.
When I had the honour to be selected umpire in the last Inter-
University Chess Match, I volunteered to the Presidents of the Oxford
and Cambridge University Chess Clubs to publish an analysis of the
positions in case I should be called upon to adjudicate on any of the
games; for I thought it undesirable, in what I believe to be a novel
manner of concluding a chess match,
That's not a surprise since according to wiki they hadn't been invented yet.
http://en.wikipedia.org/wiki/Game_clock
Going forward a number of years to just after the establishment of the BCF, there's some history on the formation of the Bristol League here.The first time that game clocks were used in a chess tournament was London, 1883.[1]
http://myweb.tiscali.co.uk/chess/THE%20 ... EAGUE.HTML
from which
The year was 1907, and on October 7th it was resolved "that steps be taken to form a league among the chess teams connected with social clubs within the Bristol Parliamentary Boundary."
Whilst I can see the logic of adjudicating games unfinished in a short session played without a clock, the 24 per hour notion would appear to have become well-established by 1907 so the logical step of dividing the available time in 2 and giving it to each player seems not to have been taken.Clocks could be insisted upon, if provided (24 moves per hour and 6 every 1/4 thereafter) and there was a minimum 2 hour playing session; unfinished games were to be adjudicated by M. H. H. Davies, whose decision was final
Was adjudication purely a British (Empire & Commonwealth) idea? How about other major chess centres of the last hundred years such as the USA, continental Europe, Czarist Russia and the Soviet Union?
I'm aware that many countries didn't play weekday night leagues, preferring weekend play like the modern leagues of France, Germany or Spain. However we did and still do have weekend team play in the UK in the form of county matches and these had move 40 (or earlier) adjudications until about 20 years ago.