What Zone 1 stations have no barriers?
The only ones I can think of are Moorgate (which is only at the temporary entrance which will be remodelled when the works are done), Bank (via a lift), Waterloo (Waterloo & City line only), Tower Gateway DLR, and some of the platforms on the Mainline station at Euston and Paddington (the former only offering a couple of destinations within the validity of CPC acceptance or used only by long distance trains, the latter almost always used only by long distance trains).
Euston Square - the lift on the Westbound Platform has no barriers, just a big sign reminding you to touch in/out.