Following some twitter accounts from the Chichester theatre people and involved with LH (like Paul Constable, Paul Arditti and many more), I saw multiple references to a theater in London called "Bridge theatre", located near the famous London bridge and the tower bridge, with a capacity of 900 people.
Looks like a very likely location for Local Hero giving that connections, and that the capacity is more than the Lyceum in Edinburgh (658) and some less than the Old Vic (1.067).
Actually, I would like that it could be that one, that's an area of London I like very very much!
I still think, as they told that by phone when they called to cancel the LH tickets, that the Old Vic could be the place again, but the Bridge Theatre looks more atractive.
Actually, at the Bridge theater, there is a play running from February to September 3rd of 2023, so it won't be possible until september next year!