If the firm is reluctant to let you book odd days holiday, then they will contrive to not let you have any to start with, eg. by giving you five or six whole weeks holiday - which has to be booked in “whole weeks” leaving no odd days.
So the trick then - is to take a week off on a bank holiday week, but to work the bank holiday itself on it’s own.
That way, you get the bank holiday credit which, in these days where firms are reluctant to pay double bubble anymore - turns into an odd day you can book whenever they’ll let you book it, the usual restrictions being that you cannot use such an odd day to take another bank holiday off!
…Then “Friday Nights” in particular, then “Monday Mornings” on non-bank holiday weeks, then finallly all the other days, which one would not expect there to be any restrictions in taking odd days on.
Thus, if you have a 4 day week that consists of UNEVEN shifts - you get to take the LONG shift off, which then not only gets you out of say, 13 hours but gives you “13 banked hours” towards your overtime aggregate you may have…
I’ve made it a personal point over all these years to work as many bank holidays as I can - so I always have the ability to take an odd day off at the drop of a hat… I was also careful not to bank-up 5 such days off - lest I be forced to take an entire week off in say, February or November.
Spreading the odd days off all around the year - usually kept me just ahead in the “banked hours aggregate” system so I could also pick up any plumb overtime I wanted as well, such as Boxing Day, New Year’s Day, and the two “Eves” which were often “half days” (job ‘n’ knock) but being paid for a full shift…
I’ve never been compelled once into working Christmas Day over the years, nor doing a night out on Fridays, and only got caught out the first time into being forced to take a week off in february, because I was banking up holidays, discouraged from doing of of course…