Well after hunting around for absolutely ages I think I have finally found what I needed for editing the data in sqlite tables, in place, in a grid.
The program is tksqlite, it takes a while to dig down to find the current version, it doesn't live in any of the normal places and, at first glance at http://reddog.s35.xrea.com/wiki/TkSQLite.html it looks as if there's nothing newer than 2006 but on digging further I found:-
http://sourceforge.net/projects/kbskit/files
... and there's recent builds there for 32-bit and 64-bit Linux. (OK, sourceforge *is* one of the usual places, but it's not at all obvious that tksqlite is there).
It does almost exactly what I want and is also a very neat sqlite3 database administration tool, much less clunky IMHO that either sqlitebrowser or sqliteman.
I just wish I could find some more complete documentation and/or a support list of some sort.