A visit from an Openreach engineer ( as you already suspect ) isn’t going to achieve much, physically there isn’t a problem, it’s much more likely to be an incomplete or messed up number port ...is the landline number originally a TT number, or was it ported into TT at some point in the past and now to be used ( or reused ) with BT ?
AFAIR there was a long running post on this forum from a ‘new’ BT customer who ported their landline number around various landline providers , and everything worked apart from incoming calls from one particular mobile provider , the last move was also from TT to BT, it appeared ( in basic terms ) that one particular mobile operator was still pushing calls for the landline number into the TT network and that call simply never terminated, the issue either with the mobile operator directing the call to the wrong place ( TT instead of BT ) , or TT not ‘rerouting’ the call towards BT when they received it, either way it was the mobile operator or TT at fault, and nothing the consumer or BT could do to get them to deal with the issue , both presumably taking the view ‘ not our customer, not our problem’.
I don’t think it was ever satisfactorily resolved....number porting seems to be something of a dark art , and in your case , if calls made on networks BT are responsible for can successfully terminate, but calls from other networks cannot, then although you ‘pay’ BT for a service, there isn’t really anything BT can do about a data error in another network operators systems.
Chances are it’s not all mobile networks affected, if possible you may want to try and arrange calls from EE, Vodafone , O2 ( and possibly 3 ) mobiles to see if it’s affecting all of these, ‘virtual’ mobile network operators like Virgin piggy back on the main 3 ( or 4 ) operators , so you shouldn’t have to consider them, unless it’s a particular mobile you have noticed the problem on, if they are a virtual operator you may have to find out who supply’s their underlying network
