s others mention, on LNER, it seems to be if reservations are not displayed, they are not valid. This was true of my last trip with them when an 800 covered for a Mark 4 set.
Realistically, issuing a penalty to someone occupying a reserved seat probably won’t happen in many cases and the BTP won’t be interested and the TOC won’t want to delay the train.
Really, if reservations were shown on the train, the member of staff should have at least asked them to move, but if not, there’s not a lot that the passengers holding the reservations can do other than write in requesting a refund/compensation afterwards.
I know of no explicit rule that the non-display of of a seat reservation notice invalidates a reservation of that seat. However, the effect of the operator's failure to display such notices is to make the seat reservation scheme unenforceable, because the presence of such notices is a prerequisite of such enforcement by exercise of the available byelaw sanctions. The 'rule' that undisplayed reservations are not valid seems to be not so much a rule as a consequence of the operator's failure to make its reservation scheme one capable of being enforced.
If, in the OP's case, there were no notices to indicate the seat reservations he had made, then my sympathy lies with those who were already occupying them. If the operator failed to alert them that their seats had been reserved by the OP, then why should they suffer inconvenience as a result of that failure?
If seat reservation notices
were on display then naturally the seats' unauthorised occupants forfeit my sympathy. If no other seats in the train were available then it was incumbent upon the operator's staff to ask them to vacate those seats so that it could fulfil its obligations to the OP under the terms of its Passenger's Charter. These terms required the operator, not the passenger, to take the initiative in rectifying the passenger's loss of his entitlements, e.g. “If you’ve reserved a seat but it’s not available, our staff
will try to find you another seat on the train.” (my emphasis). In addition it was up to staff to make the passenger aware of his entitlement to compensation, rather than leaving it to him to discover that entitlement for himself. In the OP's case a failure by LNER staff to take the positive action required of them by their employer’s Passenger's Charter should lead to a compensation award over and beyond the appropriate fraction of his ticket cost.
I can fully understand a reluctance on the part of staff to enforce seat reservations by ejection of the unauthorised occupants from the reserved seats or by reporting them with a view to prosecution for byelaw breach. However, declaring a policy in which it is implicit that a blind eye will be turned to such byelaw infractions is to encourage a perception that seat reservations can be disregarded. I'm not convinced that this is a wise course for operators to take in the long run.
In any case, the vital first step for operators to take is to ensure seat reservation notices are displayed.