I'm afraid that's not the case. Unless you you've made such journeys with Standard tickets and been removed from First Class? In which case I'm sure we could assist with a complaint.
Lets go through condition 39:
"39. Travelling in first class accommodation with a standard class ticket
If you have a standard class ticket (other than a Season Ticket), no standard class
accommodation is available, and staff on that train give their permission, then you may
travel in first class accommodation (or the equivalent) where this is available without extra
charge."
Let's assume standard class accommodation is available, as it almost certainly will be in your Beverley - Hull and Skipton - Leeds examples.
"On-train staff will not give you permission to use first class accommodation (or the
equivalent) unless they are satisfied that it is not required by anyone with a first class
ticket and the standard class accommodation on the train is full. This permission may be
withdrawn if a person holding a first class ticket requires the accommodation during your
journey or standard class accommodation becomes available."
Again, I can't see standard being full in your two examples.
"If you have a standard class ticket and you travel in first class accommodation without
permission (which includes occupying seats or standing in any part of the carriage), you
will have to pay:
(i) the difference between the price of that ticket and the price of the first class
ticket for the accommodation you have used; or
(ii) where Condition 4 (b) applies, you may be charged a Penalty Fare.
If you have a standard class Season Ticket, you may only travel in first class
accommodation (which includes occupying seats or standing in any part of the carriage) if:
(a) the difference between the full single fare for first class accommodation and the
full single fare for standard class accommodation has been paid before your
journey starts;
(b) any other relevant supplement set out in the notices and other publications of the
Train Companies has been paid before your journey starts;
(c) notices are displayed allowing passengers with standard class tickets to use first
class accommodation; or
(d) on-train ticket staff have given you permission. In all other cases, if you travel in
first class accommodation (or the equivalent) with a standard class Season Ticket,
you will be treated as having joined the train without a valid ticket and Condition 2
or 4 will apply"
In any case you would need to ask permission. You can't just sit there
"19. Classes of accommodation, reserved seats and sleeping berths
Except with permission from an authorised person, no person shall remain in
any seat, berth or any part of a train where a notice indicates that it is
reserved for a specified ticket holder or holders of tickets of a specific class,
except the holder of a valid ticket entitling him to be in that particular place. "
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/4202/railway-byelaws.pdf
I see no reason why this byelaw shouldn't apply.
Do you have a source stating that you may sit in first class accommodation with a standard class ticket just because there is no first class fare?