But surely a break of journey is allowed at Highbury & Islington, as it is a National Rail station (albeit staffed by Underground staff), which would also be why you can leave Old Street station - that also being a National Rail station.
Yes. There was disruption meaning no trains from Essex Road (ISTR a ticket there is issued to London Terminals), so we walked to Highbury & Islington to get the tube to Finsbury Park.
I was told I couldn't enter there, even though GN trains stop there so there shouldn't have been any issue as I could have been intending to use that over the tube.
I can of course see why TfL might be keen to stop people using London Terminals tickets to travel wherever they like. If the gates open, people will wrongly assume their travel is valid - and since the May timetable disruption, many more people are using the tube on the interavailable routes and may well think 'why not stay on to Euston' if they get on the Victoria line with a ticket only valid to King's Cross.
Clearly the answer is to train staff so they know from looking at a ticket if it's valid and not just assume 'seek assistance' means invalid.